Keywords: main

Next: 2.8 Contours Up: 2. Scene Description Language Previous: 2.6 Commands
Subsections

- 2.7.1 Options
  - 2.7.1.1 Sampling Quality
  - 2.7.1.2 Tessellation Quality
  - 2.7.1.3 Motion Blur
  - 2.7.1.4 Trace Depth
  - 2.7.1.5 Shadows
  - 2.7.1.6 Rendering Algorithms
  - 2.7.1.7 Feature Disabling
  - 2.7.1.8 Caustics
  - 2.7.1.9 Global illumination2.1
  - 2.7.1.10 Frame Buffer Control
  - 2.7.1.11 Scene Geometry
  - 2.7.1.12 Contours
  - 2.7.1.13 Diagnostic Modes2.1
  - 2.7.1.14 Miscellaneous
- 2.7.2 Cameras
- 2.7.3 Textures
- 2.7.4 Materials
- 2.7.5 Lights
- 2.7.6 Objects
- 2.7.7 Polygonal Geometry
- 2.7.8 Free-Form Surface Geometry
  - 2.7.8.1 Bases
  - 2.7.8.2 Surfaces
  - 2.7.8.3 Surface Derivatives
  - 2.7.8.4 Texture Surfaces
  - 2.7.8.5 Curves
  - 2.7.8.6 Trimming, Hole, and Special Curves; Special Points
  - 2.7.8.7 Space Curve Geometry
  - 2.7.8.8 Approximations
  - 2.7.8.9 Connections
  - 2.7.8.10 Example
- 2.7.9 Instances
- 2.7.10 Instance Groups

# 2.7 Scene Entities

A .mi file contains commands and scene entities in any order, with the restriction that an element must be defined before it can be referenced. All entities are named; all references are done by name. The following entities can be defined:

options | global options
camera | camera: output files, aperture, resolution, etc.
material | shading, shadows, volumes, environments, contour, etc.
texture | procedural texture or texture image
light | light
object | polygonal or free-form surface geometry
instance | places objects, lights, cameras, and groups in 3D space
instgroup | for grouping instances; the nodes of the scene DAG
shader | optional named shaders

All of these can be defined at any place, as long as they are not nested (the definition of an element must be completed before the next element can be defined). All these entities can also be incrementally changed by introducing the definition with the `incremental` keyword, which tells to re-define an existing element instead of starting a new one. The contents of the existing element become the defaults for the new one.

`options`
This element contains rendering options such as the shadow mode, tracing depth, sampling algorithm and its parameters, acceleration algorithm and its parameters, dithering and other modes.

- `camera`
  The camera is a description of the camera characteristics such as focal length and aperture that determine the field of view.

- `texture`
  Textures to apply 2D or 3D color, bump, transparency, displacement and other maps to objects. Textures are referenced by other shaders that include the texture in their color or other computation. Textures may appear verbatim in the file, or may be read from a texture file, or may be fully procedural, or a combination of these.

- `material`
  Materials describe the surface properties of objects, volumic properties of the space enclosed by objects, transparent shadow casting, environment mapping, and displacement mapping, as well as a number of property flags.

- `light`
  Lights illuminate objects and volumes. Lights are referenced in materials only (through the light instance), they are not applied directly to objects. All lights name a shading function; there are predefined shaders for points, spots, and directional lights, optionally in combination with various types of area light sources.

- `object`
  Objects describe the actual geometry. Objects may reference materials to determine the visual appearance of the surface. Various types of geometry descriptions are supported, such as polygonal objects and free-form surfaces. By default, all objects are defined in a local coordinate space ( object space), usually with the origin at the center of the object. Options exist to switch to camera space instead.

- `instance`
  When an object, light, camera, or instance group is defined, it does not become part of the scene. It must be placed in 3D space with an instance, which contains a transformation matrix, inherited parameters, and several flags. It is possible to have more than one instance reference the same object, light, camera, or instance group; this is called `` multiple instancing''. The instanced entity then appears several times in the final processed scene. It is possible to specify a `` geometry shader'' as the instanced item instead of an object. The `` geometry shader'' is expected to create a scene element which is defined in the local coordinate space of the instance.

- `instgroup`
  Instance groups are used to group instances so they can be instanced as a unit. Instance groups form the nodes of the scene DAG (Directed Acyclic Graph), which contains all entities used during processing. The instance group at the root of the DAG is called the `` root instance group.'' Since instance groups can themselves be instanced the scene DAG can be built with any number of levels and sub-DAGs, each with its own local coordinate space.

- `shader`
  Shaders are user-provided functions used for a variety of purposes. They are not normally named; they are defined where they are needed, like in a material. An unnamed shader is also called an ``anonymous shader.'' The `shader` statement allows giving a name to a shader; a named shader can be used in any place where an anonymous shader is expected by giving its name, introduced by an equals sign.

All scene entities are described in more detail in the following subsections.

## 2.7.1 Options

        options "name"
            option_statements
        end options

Options contain rendering modes. An options element must be specified to render a scene. There is a variety of option_statements that can be listed in the options. Most of them can be overridden with an appropriate command-line option; see appendix . The following option_statements are supported:

### 2.7.1.1 Sampling Quality

- `contrast` r g b [a]
  The contrast controls supersampling. If neighboring samples differ by more than the color r, g, b, a, supersampling is done as specified by the sampling parameters (see below). Default for a is the average of r, g, and b. The recursive supersampling algorithm controlled by `samples` modifies the contrast based on the recursion level: at sample level 0, the contrast is used directly; at sample level 1, the contrast is doubled (effectively requiring a higher contrast to force another subdivision), and so on. Negative levels divide the contrast, i.e. use a fraction 12, 14, and so on. In general, the contrast is multiplied by 2level at the supersampling level level, which is bounded by `samples`. The default is 0.1 0.1 0.1 0.1.

- This is the primary means of image quality control. Typically values are 0.1 for r, g, b, and a. Values such as 0.2 or 0.3 reduce quality; lower values increase quality. Values less than 0.05 do not further increase quality in most cases. r, g, b, a can be specified separately to allow physiologically correct contrast values; the human eye is much more sensitive to different shades of green than blue and red, and can only poorly distinguish shades of blue. The a value should be set to 1.0 if the matte (alpha) channel is not needed; it is also possible to set a lower than r, g, b to generate matte channels with a higher quality than the color image. If the a value is missing, it is set to the average of r, g, b. Note that for high-quality rendering, the `samples` parameters must be adjusted.

- `time contrast` r g b [a]
  The time contrast controls temporal supersampling for motion blurred scenes. It works similar to the spatial contrast parameter explained above: If neighboring samples in time differ by more than the color r, g, b, a, supersampling is done. Default for a is the average of r, g, and b. Using values for `time contrast` that are higher than `contrast` can speed up motion blur rendering at the price of more grainy images without degrading the quality of spatial antialiasing. The default is 0.2 0.2 0.2 0.2; much higher than the spatial contrast.

- `samples` [minint] maxint [`view`]
  This statement determines the minimum and maximum sample rate. Each pixel is sampled at least 22 . min times and at most 22 . max times in each direction. If min is 0, each pixel is sampled at least once. Positive values increase the sample rate; negative numbers reduce the sample rate to less than one initial sample per pixel ( infrasampling). min defaults to -2, which means that at least one sample per 4 `x` 4 pixels is taken. If min is chosen too small, small features may be lost if all samples happen to miss it (if it is found just once in any pixel of a task, will analyze the feature and render it correctly).

- If `view` is specified, sample view mode2.1is turned on. In this mode, the rgb image will be replaced with an image that shows where samples were collected during rendering. This is useful for tuning the min and max values, and the `contrast` option and identifying troublesome areas in the image. A pixel's intensity reflects the number of samples collected within the pixel and on its bottom and left edges. It is normalized to the maximum number of samples per pixel. In addition, task boundaries are shown in red in the image.

- If no min value is given, max - 2 is used by default. The defaults for min and max are -2 and 0, respectively. It is recommended to use max values larger than or equal to min + 2; the difference should not be higher than 3. Typical values for min and max are -20 for low-quality preview rendering, -11 for medium-quality rendering, and 02 or 13 for high-quality renders. Note that while this option offers simple control of rendering quality, it is recommended to control quality with the `contrast` option, which allows much finer control and deals more gracefully with high-contrast cases where the `samples` option can leave aliasing due to the hard cutoff. The `samples` statement should be used only as a hard sampling limit.

- If a `filter` camera statement is used to set a filter other than `box 1 1`, min and max must be set to at least 1 1 for 2.0, or at least -1 0 for 2.1 or later.

- `filter box|triangle|gauss|mitchell|lanczos` [width [height]]
  The filter statement specifies how multiple samples are to be combined into a single pixel value. The filter defaults to a box filter of width and height 1.0, which is the fastest of the filters. This option allows changing the filter kernel or the filter size. The available kernels are: box, triangle, Gauss, Mitchell2.1, and Lanczos2.1. The size of the filter is specified in pixel units. If no height is given it is taken to be equal to the width. Filters must be larger than 0.0. If the size of the filter is not specified, default values are used. These are 1.0 for box, 2.0 for triangle, 3.0 for Gauss and 4.0 for Mitchell and Lanczos. The default height is the same as the default width. Larger filter sizes result in softer images and may reduce rendering speed slightly, while values smaller than the defaults can introduce artifacts. Filters must be larger than 0.0 but sizes smaller than 1.0 are generally wasteful since they will discard some samples.

- The box filter sums all samples in the filter area with an equal weight. The triangle filter functions has the shape of a pyramid centered on the pixel, which means that samples at the center of a rendered image pixel contribute more than more distant samples. The Gauss filter weights the samples using a Gauss curve that is cut off at an ellipse centered on the pixel. The Mitchell and Lanczos filters are both approximations of the theoretically ideal sinc filtering function, cut off after its second lobe. In most cases, the Mitchell filter gives better results. For these two, a filter width of 4.0 corresponds to a frequency cutoff of 2.0 pixels, the Nyquist frequency. In order to use non-default filters, the limits for the `samples` statement must specify min = - 1 or greater, and max = 0 or greater ( 2.0: 1 1 or greater). Otherwise a warning will be printed and the `filter` statement ignored.

- `jitter` jitter
  The jittering factor introduces systematic variations into sample locations. Without jittering, samples are taken at the corners of pixels or subpixels. Jittering displaces the samples by an amount calculated by lighting analysis. This is used to reduce artifacts. Jittering is turned off by default, or by specifying a jitter of 0.0. To turn jittering on, use a jitter value of 1.0. Jittering works best in ray tracing mode.

### 2.7.1.2 Tessellation Quality

- `approximate` technique [minint maxint] `all`
  This statement overrides all approximations for base surfaces (i.e. the surface before applying displacement), free-form surfaces or polygons, in geometric objects. See section for a more detailed description of approximations. Here is a brief summary of technique, which is a list of one or more of the following:

- `view`
  `tree`
  `grid`
  [`regular`] `parametric` u_subdiv [v_subdiv]
  `length` edge
  `distance` dist
  `angle` angle
  `spatial` edge
  `curvature` dist angle

- Like in object approximation statements, the subdivision limits min and `max` can be specified how often a triangle can be subdivided. The defaults for min and max are 0 and 5, respectively; 5 is a very high value because every increment of 1 can quadruple the number off triangles in the extreme case. In objects, the approximation technique is followed by the surface or curve it applies to; in the options the keyword `all` indicates that an option approximation overrides all object approximations.

- `approximate displace` technique [minint maxint] `all`
  This statement overrides all approximations for displacement maps in geometric objects. Both kinds of approximation overrides are useful for temporarily reducing tessellation quality for previews to reduce tessellation and rendering time without redefining all objects, for example by specifying

- `approximate regular parametric 1.0 1.0 0 2 all`
  `approximate displace regular parametric 1.0 1.0 0 2 all`

### 2.7.1.3 Motion Blur

- `shutter` shutter
  This statement specifies the shutter open time. A shutter value of 0.0 turns motion blurring off, and values greater than 0.0 turn motion blurring on. The shutter value scales the motion vectors attached to object vertices or computed from motion transformations. If shutter is 1.0, each vertex moves the distance given by its motion vector, and is blurred in the image over this distance. Values less than 1.0 reduce the length of this path.

### 2.7.1.4 Trace Depth

- `trace depth` reflectint [refractint [sumint]]
  The reflect parameter limits the number of recursive reflection rays. If it is set to 0, no reflection rays will be cast; if it is set to 1, one level is allowed but a reflection ray can not be reflected again, and so on. Similarly, refract controls the maximum depth of refraction and transparency rays (which implement transparency with and without index of refraction). Additionally, it is possible to limit the sum of reflection and refraction rays with sum. For example, if `3 3 4` is given, an eye ray may be reflected 3 times, or refracted 3 times, or reflected twice and then refracted twice, or any other combination that sums up to at most 4. The defaults are 2 2 4. Note that custom shaders may override these values.

### 2.7.1.5 Shadows

- `shadow off`
  This statement disables all shadows.

- `shadow on`
  Simple shadows are enabled. This is the most efficient and least flexible of the three shadow modes. If shadows overlap because multiple objects obscure the light source, the order in which these objects are considered (and their shadow shaders are called) is undefined. If one object is found to completely obscure the light, no other obscuring objects are considered. This statement turns off shadow sorting and shadow segments. Also see `shadowmap motion` below.

- `shadow sort`
  This shadow mode enables shadow sorting. It is similar to the preceding shadow mode, but ensures that the shadow shaders of obscuring objects are called in the correct order, object closest to the illuminated point first. This mode is slightly slower but allows specialized shaders to record information about obscuring objects. If no such special shader is used, this mode offers no advantage over simple `shadow on`.

- `shadow segments`
  Like with `shadow sort`, the shadow shaders are called in order. Additionally, shadow rays are traced much like regular rays, passing from one obscuring object to the next, from the light source to the illuminated point. Each such ray is called a shadow segment. This slows down rendering, but is required if volume effects should cast shadows (such as certain complex shaders like fur and smoke volume shaders). This mode requires support from the shadow shader, which must use the mi_trace_shadow_seg function to cast the next shadow ray segment.

- `shadowmap on|off|opengl`
  This flag turns shadow maps on or off for the entire rendering. Shadow map parameters are specified for each light source. The default is off because shadow maps, while often significantly faster, always assume opaque objects. opengl2.1mode causes mental ray to use OpenGL acceleration if available when rendering shadow maps. The same limitations apply as mentioned with the `scanline` option. Additionally, because of the difference of the rendering algorithm, shadow maps rendered with this option contain slightly different information from those generated with the regular algorithm, and the resulting shadows may look different. In particular, soft areas of shadows tend to be smaller and some areas may incorrectly be determined to be not in shadow. When OpenGL rendering of shadow maps is enabled, only the client host will participate, since the computation cost of the map is so small that the network transfer costs could not be recovered.

- `shadowmap rebuild on|off`
  Determines whether all shadow maps should be recomputed. If this option is off (the default) shadow maps are loaded from files or reused from previously rendered frames if possible. If this option is on, no shadow map is reused - everything is recomputed. The default is off.

- `shadowmap motion on|off`
  Determines whether shadow maps should be motion blurred such that moving objects will cast shadows along the path of motion. Turning this option off can improve performance of rendering shadow maps slightly faster. The default is on. Note that since shadow maps do not deal with transparent objects and motion blurring introduces a form of transparency at the edges, shadow map shadows can appear too large in the direction of motion if the object moves quickly.

### 2.7.1.6 Rendering Algorithms

- `trace on|off`
  Normally, will use a combination of a scanline algorithm and ray tracing to calculate samples of the scene. If `trace off` is specified, ray tracing is disabled, and will rely exclusively on the scanline algorithm. Since the scanline algorithm can only compute straight rays from the pinhole camera, reflection rays cannot be cast and refraction rays are computed like transparent rays, which do not allow control over the ray direction based on the index of refraction of the material. Lens shaders cannot alter the ray origin and direction. However, reflections onto environment maps do work. Motion blurring and shadows are also affected if ray tracing is turned off. Ray tracing is turned on by default.

- `scanline on|off|opengl`
  This statement allows turning off the scanline algorithm. By default, tries to use a scanline algorithm for straight rays from the pinhole camera, such as primary rays. In most cases this gives better performance than pure ray tracing. Turning scanline off forces to rely entirely on ray tracing. This will generally slow down rendering but in some cases, for example when the `task size` is very small, the overhead of initializing the scanline algorithm may outweigh its benefit and turning it off can result in an improvement in speed. The opengl2.1option will cause mental ray to use OpenGL hardware if present to further accelerate rendering. If possible, the master host will use OpenGL to generate acceleration data that the scanline algorithm then uses for intersection testing. Also see `task size` below.

- `acceleration bsp`
  Selects the binary space partitioning ( BSP) ray tracing algorithm. This algorithm is often, but not always, faster. It is controlled by the `bsp size` and `bsp depth` statements. The BSP algorithm is the default.

- `acceleration grid`
  Selects the grid rendering algorithm. It provides faster preprocessing especially on multiprocessor systems. Memory usage is more conservative and much easier to control than with the BSP algorithm. Speed is comparable to BSP but more scene-dependent. It is controlled by the `grid size` statement.

- `acceleration raycl`
  Selects the ray classification ray tracing algorithm. Like the grid algorithm, this algorithm operates with a constant acceleration memory size. This size is controlled by the `raycl memory` and `raycl subdivision` statements. It only works in camera space scenes and exists mainly for backwards compatibility with 1.x.

- `bsp size` sizeint
  The maximum number of primitives in a leaf of the BSP tree. This statement is used only if binary space partitioning is enabled. It has no effect on the other algorithms. Larger leaf sizes reduce memory consumption but increase rendering time. The default is 4.

- `bsp depth` depthint
  The maximum number of levels in the BSP tree. This statement is used only if binary space partitioning is enabled. Larger tree depths reduce rendering time but increase memory consumption, and also slightly increase preprocessing time. The default is 24. If there are too many triangles in the scene to fit into the BSP tree with the size specified by `bsp size` and `bsp depth`, the `bsp size` value is disregarded and larger leaves are created. This slows down rendering significantly. Larger `bsp depth` values of 30, 40, or even 50 often massively improve rendering speed in BSP mode for larger scenes. The mental ray User's Manual discusses how to choose good parameters in detail.

- `bsp memory` memoryint
  The maximum memory in megabytes used in the BSP preprocessing. A value of zero indicates that there is no limit on the memory consumption, this is the default. This flag is useful only on multiprocessor machines since the memory consumption increases with the number of rendering threads. When the specified amount of allocated memory is reached, will prevent threads from being scheduled for preprocessing, thus reducing the memory requirements. The BSP tree itself is unaffected.

- `raycl subdivision` subdivint subdiv_2dint
  If ray classification is enabled, uses a ray tracing algorithm that subdivides the space of all rays. The optimal subdivision is determined automatically by a built-in scene analysis. The `raycl subdivision` statement can be used to modify the result of this analysis: arguments of 0 leave the calculated subdivision unchanged, positive numbers increase and negative numbers reduce the subdivision. subdiv controls general subdivision; subdiv_2d controls primary (eye) and shadow rays. This option has no effect if the BSP or grid algorithms are used.

- `raycl memory` memoryint
  In ray classification mode, this statement sets the amount of memory to be used for acceleration data structures to memory megabytes on each CPU. It has no effect if the BSP or grid algorithms are used. allows presetting the amount of rendering acceleration memory independently of scene complexity without sacrificing speed. The default is set to 6 megabytes, which is sufficient for most scenes. Even for extremely large scenes, little can be gained from memory sizes greater than 12 megabytes. Note that this statement does not affect the amount of memory used for the scene description, which depends on the complexity of the geometry in the current frame.

- `grid size` sizeint
  If the grid algorithm is used, this option adjusts the scene-dependent default grid voxel size. The default is 1.0. Larger values increase the number of voxels and shrink each voxel accordingly. Smaller voxels are faster to render because they contain fewer triangles to be tested, but larger numbers of voxels require more memory and long rays pass through more voxels that need to be tested.

### 2.7.1.7 Feature Disabling

- `lens on|off`
  Ignore all lens shaders if set to `off`. The default is `on`.

- `volume on|off`
  Ignore all volume shaders if set to `off`. The default is `on`.

- `geometry on|off`
  Ignore all geometry shaders if set to `off`. The default is `on`.

- `displace on|off`
  Ignore all displacement shaders if set to `off`. The default is `on`.

- `output on|off`
  Ignore all output shaders if set to `off`. The default is `on`. File output statements are not affected. Note that all five disable options also affect shaders installed by phenomena. This means that the phenomenon can fail if it installs cooperating shaders that rely on each other's existence, and one of them is disabled with these options. Phenomenon writers must allow for this case. The purpose of these options is fast preview rendering.

- `merge on|off`
  Ignore all merge epsilons and all connections in the scene.

### 2.7.1.8 Caustics

- `caustic on|off`
  Caustics are turned on or off. They are off by default. Caustics are lighting effects caused by specular focusing of light rays, such as the irregular light patterns on the floor of a swimming pool. Note that caustics are only computed for light sources that specify an energy explicitly. The material shader that receives the caustics must also cooperate, and either the options block or the object to receive caustics must have appropriate `caustic` flag set.

- `caustic accuracy` N [R]
  This option controls how caustics are estimated from the photon maps during rendering. The photon map is searched outwards from the intersection point and the photons that are encountered are examined. N specifies the maximum number of photons that should be examined, and R specifies the maximum radius that is searched for photons. If N is zero, the number of photons is only limited by R. The default for N is 100. If R is zero, a scene-size dependent radius is used instead. This is the default.

- `caustic filter box|cone` [filter_const]
  Filtering controls the sharpness of the caustics. Specifying a cone filter with the default filter_const of 1.1 generally has the effect that the caustics in the model looks sharper. Increasing the filter_const makes the caustics more blurry and decreasing makes it even sharper but also slightly more noisy. The filter_const must be larger than 1.0.

- `photon trace depth` reflectint [refractint [sumint]]
  This option is similar to the `trace depth` option except that it applies to photons, not rays. The reflect parameter limits the number of recursive reflection photons. If it is set to 0, no photons will be reflected, if it is set to 1, one level is allowed but a photon cannot be reflected again, and so on. Similarly, refract controls the maximum depth of refracted photons. Additionally, it is possible to limit the sum of reflected and refracted photon levels with sum. Note that custom shaders may override these values.

- `photonmap file "`filename`"`
  Tells to use the file filename for the photon map. If the photon map file does not exist, it is created and the photon map is saved. If it exists, it is loaded and used without computing a new photon map.

- `photonmap rebuild on|off`
  If a filename is specified for the photon map (using the `photonmap` filename option) it is normally loaded and used if the file exists. If the `photonmap rebuild` option is turned on, any existing file will be ignored, and the photon map will be recomputed and an existing file will be overwritten. The default is off.

### 2.7.1.9 Global illumination2.1

- `globillum on|off`
  Global illumination2.1is turned on or off. The default is off. Global illumination permits effects such as indirect lighting, color bleeding, etc. See the User's Manual for details. Note that global illumination is computed only for light sources that have an energy specified explicitly; see section for details. The material shader that receives global illumination must also cooperate.

- `globillum accuracy` N [R]
  This option controls how the photon map is used to estimate the intensity of global illumination. For a more detailed discussion of how this works, see the `caustic accuracy` option above. The default values are N = 500 and R = 0.0. For fast previews of global illumination, it can be useful to set N to 100.

- `photonvol accuracy` N
  This option controls how the photon map is used to estimate the intensity of caustics or global illumination within a participating medium. It applies to photon volume shaders, which compute light patterns in 3D space, such as volume caustics created by focused shafts of light cast by objects acting as lenses. The details are similar to what is described for the `caustic accuracy` option above. The default values are N = 30 and R = 0.0.

`photon trace depth`, `photonmap`, and `photonmap rebuild on|off` have the same meaning as for caustics.

- `finalgather on|off`
  Final gathering2.1for global illumination is turned on or off. The default is off. Final gathering means that when the illumination is computed at a diffuse point, the hemisphere above the point is sampled for indirect illumination. The illumination at those points is then computed as direct illumination plus a contribution from the photon map if global illumination is on. Final gathering is best suited for scenes with slow variation in indirect illumination, for example purely diffuse scenes. Final gathering eliminates the low-frequency variation in the global illumination that can often be seen if too few photons are used. Performance is kept acceptable by reusing and interpolating nearby final gathers. (Without final gathering, global illumination is computed by direct lookup in the photon map at the point -- similar to the way caustics are computed.)

- `finalgather accuracy` N [R1 [R2]]
  N controls how many rays should be used in each final gathering step to compute the indirect illumination. The default is 1000. Increasing this number makes the indirect illumination less noisy but also increases the rendering time. R1 is the maximum radius in which a final gather result can be interpolated or extrapolated. The default maximum radius is computed based on the scene extent. R2 is the distance within a final gather result must be used for interpolation or extrapolation. The default is 10% of the maximum radius.

### 2.7.1.10 Frame Buffer Control

- `colorclip rgb|alpha|raw`2.1
  This option controls how colors are clipped into a valid range [0, 1] before being written to a non-floating point frame buffer or file. The `rgb` mode is the default. In this mode, RGB is first clipped to [0, 1] and alpha subsequently to [max(R, G, B), 1]. In `alpha` mode, alpha is first clipped to [0, 1] and RGB subsequently to [0, A]. In `raw` mode, RGB and A are both clipped to [0, 1] independently of each other. In all modes, the RGB components are clipped as specified by the `desaturate` option. The `rgb` and `alpha` modes ensure that the resulting color is a valid premultiplied color. `rgb` should be used if the alpha channel is considered less important than preserving the RGB color and intensity. `alpha` mode is intended for alpha compositing, where the alpha channel is more important than the absolute color value to preserve correct transparencies. `raw` mode should only be used if no layering based on alpha is going to take place. This mode also forces the `premultiply` mode to `on`. It should be used with care because shaders might receive ``illegal'' colors (colors that cannot be composited in standard ways).

- `desaturate on|off`
  If a color is output to a frame buffer that does not have 32-bit (floating-point) precision, and its RGB components are outside the range [0, max], mental ray will clip the color to this legal range. If desaturation is turned off, the individual components are simply clipped into range. Otherwise, tries to maintain the brightness of the color by moving it towards the grayscale axis of the color cube, until the RGB components are in the legal range. max is determined by the `colorclip`2.1mode. Desaturation is turned off by default.

- `premultiply on|off`
  Premultiplication means that colors are stored with alpha multiplied to R, G, and B. For example, white at 10% opacity is not stored as (1, 1, 1, 0.1) but as (0.1, 0.1, 0.1, 0.1). This is the standard method in computer graphics to represent colors; mental ray always uses it internally and in all shaders. One implication is that R, G, and B can never exceed A. mental ray normally enforces this when storing color values into frame buffers. The `premultiply off` option instructs mental ray to always store colors unpremultiplied into frame buffers and files. It does this by undoing the internally applied premultiplication. (mental ray internally always works with premultiplied colors to present a uniform interface to shaders; since this is done with floating-point values there is no precision penalty.) This option is ignored if the `colorclip raw`2.1mode is in effect.

- `dither on|off`
  supports 8, 16, or 32 bits per color component. In some cases, 8 bits per pixel, as supported by all popular picture file formats, can cause visible banding when the floating-point color values calculated by the material shader are quantized to the 8-bit values used in the picture file. Dithering mitigates the problem by introducing noise into the pixel such that the round-off errors are evened out. Note that this can cause run-length encoded picture files to be larger than without dithering. Dithering is turned off by default.

- `gamma` gamma_factor
  Gamma correction can be applied to rendered color pixels to compensate for output devices with a nonlinear color response. All R, G, B, and alpha component values are raised to 1overgamma_factor. The default gamma factor is 1.0, which turns gamma correction off.

- `frame buffer` n [`"`type`"`]
  Define or delete user-defined frame buffer2.1n. Up to eight user frame buffers are supported, numbered 0 through 7. The frame buffer type type may be any standard image type allowed in an output statement, such as rgba or `z`. If the type is prefixed with a ```+`'' sign, samples are interpolated; if prefixed with a ```-`'' sign, it is padded. Padding is the default for all types. For example, `+rgba_fp` is an interpolated floating-point color frame buffer. After a frame buffer is defined, it may be used as the type `fb`n, with n in the range 0...7, in output statements in cameras. The frame buffer is created in memory during rendering only if it is referenced by at least one output statement.

### 2.7.1.11 Scene Geometry

- `camera space`
  All geometry is expected to be defined in camera space. Camera space assumes that the camera is at the coordinate origin (0, 0, 0) and looks down the negative Z axis. This means that geometry will typically have negative Z coordinates. This is the default. In camera space mode, instance transformations have no effect.

- `object space`
  All geometry is expected to be defined in object space. Each object, light, and camera has its own coordinate space, typically but not necessarily with the coordinate origin (0, 0, 0) in the center of the object. The object coordinate coordinate space is positioned and oriented in world space with the instance transformation matrix (every object, light, and camera requires an instance). Object space allows multiple instancing where the object is placed in the scene more than once using multiple instance entities.

### 2.7.1.12 Contours

- `contour store` shader
  If the camera contains a contour output statement (see the User's manual, contour rendering is enabled and a contour store shader must be defined. This function stores information about the future contour edge, such as color, depth, normal, and other local information that is later used by the contour contrast shader to decide where the contour lines should be drawn, and by contour shaders to decide which colors and thicknesses the contours should have. Shader lists are not allowed here.

- `contour contrast` shader
  If contour rendering is enabled, a contour contrast shader must also be defined. It decides where the contour lines should be drawn based on values stored by contour store shaders. The contrast shader compares two such value sets at a time. See the User's Manual for details. Shader lists are not allowed here.

### 2.7.1.13 Diagnostic Modes2.1

- `diagnostic grid off|object|world|camera` S2.1
  Draws a colored grid on all objects in the scene visualizing the coordinate space given. The distance between grid lines is S units. This is useful to estimate the size and distances between objects and to visualize the object space of objects. The `off` argument turns this mode off.

- `diagnostic photon off|density|irradiance` N2.1
  When using photon maps, this mode replaces all material shaders in a scene with an internal shader that produces a false-color rendering of photon density, or the average of the red, green, and blue irradiance components. Photon density is the number of photons per unit surface area. N is the density (or irradiance) that is assigned to 100%, or red. The colors are, from 0% to 100%: blue, cyan, green, yellow, and red. Higher values fade to white. N can be given as zero in which case the appropriate maximum is automatically found. This mode is useful when tuning the number of photons in a photon map and setting the various `accuracy` options, since the density (or irradiance) is estimated using those settings. The `off` argument turns this mode off.

- `diagnostic samples on|off`2.1
  This mode replaces the rendered image with a grayscale image showing the number of image samples made for each pixel. A black pixel has had no samples, whereas a white pixel has had the maximum amount as specified with the `-samples` option. In addition, a red grid is drawn indicating task boundaries. Samples that lie exactly on pixel boundaries are considered to belong to the lower and/or left pixel. This mode is useful when tuning the `samples` and the `contrast` options for optimal effect.

### 2.7.1.14 Miscellaneous

- `face front|back|both`
  The front side of a geometric object in the scene is defined to be the side its normal vector points away from. By specifying that only front-facing triangles are to be rendered, speed can be improved because fewer triangles need to be tested for a ray. This works well unless there are objects whose back side is seen by refracted or reflected rays - with `face front`, the back side would not be visible. The default is `face both`, and works best if volume effects are used, which usually depend on closed volumes.

- `task size` sizeint
  This option specifies the size of the image tasks during rendering. Smaller task sizes are convenient for previewing, but also increase the overall rendering time. This option can also be used in order to optimize load balancing for parallel rendering. If the `task_size` is not specified, an appropriate default value is used. Note that very small task sizes can cause the scanline algorithm to perform poorly and in such cases it may be desirable to turn it off. See `scanline` above.

- `inheritance "`function_name`"`
  To use parameter inheritance, a user-provided inheritance shader must be specified. The function_name is the name of a C function linked to using a `link` command. No user-defined parameters are passed. The inheritance shader is called for every pair of instances of which one is the parent (one level higher up in the scene DAG) of the other. The inheritance shader must compute a set of inherited parameters from the parameters stored in these two instances. It is called even for the instances that contain no parameters and for top-level instances; in this case the corresponding parameter argument pointer is zero. Inheritance shaders are not regular shaders; they are usually written by translator writers who need to emulate the inheritance methods used by the language to be translated.

## 2.7.2 Cameras

        camera "name"
            camera_statements
        end camera

A camera describes a view of the scene, including the list of files to write, the lens shaders to use, volume shaders to be used as the global atmosphere or fog, global environment shaders that control what happens to rays that leave the scene, and other parameters. Cameras are scene entities that need to be placed in the scene with an instance element. In object space mode (see `options` element above), the location of the camera in world space is determined by the camera instance transformation. Note that the camera instance must be attached to the root instance group of the scene. See below for information on instance groups.

Cameras contain output statements that specify output shaders and output files to write to disk, and control which frame buffers creates and maintains during rendering. More than one output file can be created, and output shaders such as filters can be listed that operate on the final rendered image, before it is written to a picture file. outputs is one or more output statements. Output statements are very similar to shader lists, like lens shader statements, but the syntax is different to allow type specifications and output file names:

        output  ["datatype"]   "filetype"   [options]   "filename"
        output  "datatype"   "shader_name"   (parameters)

The first kind writes a picture to a file named filename, using the file format filetype. Normally, file formats imply a data type, but the defaults can be overridden by naming an explicit datatype. For example, the file type `"rgb"`, which stands for a SGI RGBA image file, implies the data type `"rgba"`.

The options specify additional format related parameters. Currently, the `"jpg"` file format supports one option `quality`2.1q, where q is an integer value between 0 and 100. Lower values force higher lossy compression resulting in lower image quality. A quality value of 0 will cause the use of the default quality 75.

The second kind of output statement calls an output shader, such as a filter, that may operate on all available frame buffers. Here, the datatype may be a comma-separated list of types if the shader requires multiple frame buffers. Each type can be prefixed with a ``+'' or ``-'' to turn interpolation on or off. Interpolation is averaging for color, depth, and normal images and max'ing for label images. Interpolation is on by default for the standard color frame buffer and off by default for all others. For example, a shader that filters the standard RGBA image with a filter whose size depends on the distance of objects needs both the interpolated RGBA buffer and the interpolated depth buffer, and would have a data type `"rgba,+z"`. creates all types of frame buffers requested by at least one output statement of either kind.

The data types `"fb0"` through `"fb7"` refer to user frame buffers2.10...7. User frame buffers are defined in the options statement using `frame buffer` statements. The actual data type of `fb`n is the type of frame buffer n. For example, the output statements

         output "+rgba" "rgb"  "file1.rgb"
         output "fb0"   "ctfp" "file2.ct"

write the standard frame buffer to the image file `file1.rgb`, and then write the contents of user frame buffer 0 to the image file `file2.ct`. This assumes that the options block contains a statement that defines user frame buffer 0, such as:

         frame buffer 0 "+rgba_fp"

User frame buffers are empty unless some shader writes to them during rendering. Their purpose is to collect nonstandard image data during rendering, and making the data available for output shading and image file writing.

A special data type `"contour"` can be specified that enables contour rendering. Special contour output shaders must be specified that pick up the contour information from the contour cell frame buffer and compute a color image, which it can either put into the regular color frame buffer, or composite on top of the color frame buffer. In the latter case, one rendering phase creates a color image with contours. The color frame buffer can then be written to an image file using a regular image output statement. There is also a built-in contour output shader that creates a PostScript file instead of a color image. See the Contour chapter in this manual for details and examples.

There is a variety of camera_statements that can be listed in the camera. Some of them can be overridden by specifying an appropriate command-line option; see appendix .

There are four camera statements that accept shader lists: `output`, `lens`, `volume`, and `environment`. As with all types of shaders, more than one shader can be listed, or more than one such statement can be given, to attach multiple shaders (or output files in the case of the `output` statement) to each type. In an incremental change (the `incremental` keyword is used before the `camera` keyword), each of the four first resets the list from the previous incremental change and does not add to the existing list, as multiple statements inside the same `camera` ... `end camera` block would.

The following camera_statements are supported:

- `focal` distance`| infinity`
  The focal distance is set to distance. The focal distance is the distance from the camera to the viewing plane. The viewing plane is the plane that the rendered scene is projected onto; its edges correspond to the edges of the rendered image. A common approach is to set the focal distance to the middle distance of the interesting objects in the scene and then set the aperture such that it is a bit larger than the horizontal extent of the objects in camera space. If `infinity` is used in place of the distance, an orthographic view is rendered. An orthographic view turns off perspective, all camera rays are parallel. View-dependent surface tessellation is not possible in orthogonal mode.

- `aperture` aperture
  The aperture is the width of the viewing plane. The height of the viewing plane is aperture divided by aspect. Together with the `focal` and `aspect` viewdefs, `aperture` defines the lens of the standard pinhole camera.

- `aspect` aspect
  This is the aspect ratio of the camera. The default is 1.33. In camera space, aperture is the width of the viewing plane and aperture divided by aspect is the height. The viewing plane is divided into pixels as specified by the `resolution` viewdef, so the aspect will result in nonsquare pixels if it is not equal to the X resolution divided by the Y resolution. For example, to render a PAL image at a resolution of 720 `x` 576 pixels, at an image ratio of 3:4 as defined by the PAL standard, pixels are slightly wider than tall, by a factor of . = 1.0667. If the aspect ratio is corrected by this number, objects will appear undistorted on a PAL video display (but not on a computer display with square pixels).

- `resolution` xint yint
  Specifies the width and height of the output image in pixels.

- `offset` x y
  Specifies an offset2.1for the rendered image. The default is 0.0 for both values, which means that the image will be centered on the camera's Z axis. Positive values translate the image up and to the right. The offset is

- `window` x_lowint y_lowint x_highint y_highint
  Only the sub-rectangle of the image specified by the four bounds will be rendered. All pixels that fall outside the rectangle will be left black.

- `clip` hither yon
  The hither (near) and yon (far) planes are planes parallel to the viewing plane that delimit the rendered scene. Points outside the space between the hither and yon planes will not be rendered (this does not apply to the infinite-radius environment maps because they are not geometric objects). The `clip` statement specifies the distance of the hither and yon planes from the camera. The defaults are 0.0001 for the hither distance and 1000000.0 for the yon plane.

- `volume` [shader_list]
  This statement specifies volume (atmosphere) shaders. The atmosphere affects all rays passing through the space outside objects by attenuating the color of the ray. It is possible to specify a volume shader for the inside of objects too, by naming a volume shader in the `material` statement (see above). If no shader_list is specified, the existing volume shader list is deleted; this is useful in incremental changes. If a list is given, it replaces the current list if this is the first `volume` statement in the camera block, or it is appended to the current list otherwise.

- `environment` [shader_list]
  This statement specifies environment shaders. Environment shaders control the color returned by primary rays that, after leaving the camera, never strike any object in the scene. They are similar to environment shaders named in materials, which control reflection rays cast by the material shader that leave the scene without striking another object (or exceeding the trace depth). If no shader_list is specified, the existing volume shader list is deleted; this is useful for incremental changes. If a list is given, it replaces the current list if this is the first `volume` statement in the camera block, or it is appended to the current list otherwise.

- `lens` [shader_list]
  Lens shaders simulate lenses by changing the camera. If no lens shader is present, the camera is a pinhole camera that casts rays from the origin in all directions that strike the viewing plane, or an orthographic camera that casts parallel rays if `focal infinity` is specified. A lens shader accepts the origin and direction of the camera ray, modifies them, and casts a new primary ray. Examples for lens shaders includes fish-eye lenses that exaggerate the direction vector in a nonlinear way (there is a code example in the Shader section). Multiple lenses can be specified in the camera; the n-th lens shader receives the origin and direction computed by the n - 1st lens shader. If no shader_list is specified, the existing volume shader list is deleted; this is useful in incremental changes. If a list is given, it replaces the current list if this is the first `volume` statement in the camera block, or it is appended to the current list otherwise.

- `frame` frameint [time] [`field` fieldint]
  Every camera should contain the current frame number frame. The time in seconds can optionally be specified as time. Optionally, a field number field can be specified; by convention, field should be 0 when rendering frames, 1 when rendering the first (odd) field, and 2 when rendering the second (even) field. If the `field` modifier is missing, the field number defaults to 0. mental ray currently does not use any of these values but makes them available to shaders.

## 2.7.3 Textures

        scalar texture "texture_name" [widthint heightint [depthint] ] bytes ...
        [ local ] [ filter [scale_const]] scalar texture "texture_name" "filename"
        scalar texture "texture_name" shader_list

        color texture "texture_name" [widthint heightint [depthint] ] bytes ...
        [ local ] [ filter [scale_const]] color texture "texture_name" "filename"
        color texture "texture_name" shader_list

        vector texture "texture_name" [widthint heightint ] bytes ...
        [ local ] vector texture "texture_name" "filename"
        vector texture "texture_name" shader_list

Textures are lookup functions. They come in two flavors: lookups of two-dimensional texture or picture files or literal bytes, and procedural lookups. File textures require a file name parameter or a byte list; procedural textures require a shading function parameter. There are three types of texture functions: textures computing scalars, colors, and vectors. Which one is chosen depends on what the texture is used for. Textures are used as parameters to other shaders, typically material shaders. A material shader could, for example, use a color texture to wrap a picture around an object, or a scalar texture as a transparency or displacement map, or a vector texture as a bump map. The actual use of the texture result is entirely up to the shader that uses the texture.

All of the above syntax variations define a texture texture_name. The texture_name should be quoted to avoid reserved words and to allow non-alphabetic characters. This is the name that the texture will later be referenced as.

Non-procedural textures can be defined by specifying the width and height of the texture and an optional depth (bytes per component, 1 or 2, default is 1), followed by a list of width `x` height `x` depth hexadecimal two-digit bytes, most significant digit first if depth is 2, in RGBA order for colors and UV order for vectors. Note that the brackets around the sizes are literally part of the `.mi` file, while the skinny brackets around depth denote that the depth is optional and are not part of the `.mi` file.

Non-procedural textures can also be defined by naming a texture or picture file. For a list of allowed file formats, see the section on Available Output File Formats. In this case, the sizes (width, height, and depth) are read from the file. If the `local` keyword is not present, the file is read once on the client host and then transmitted over the network to all server hosts that participate in the rendering. With the `local` keyword, only the file name is transmitted to the server hosts; this requires the file exists locally on all server hosts but reduces network transfer times drastically if many texture files or very large texture files are used. Filename rewriting is available for interpreting the remote filename locally, for example to translate between Unix and Windows NT paths. Maximum speed improvements are achieved if local files reside on physical disks and not on NFS-mounted file systems (NFS stands for Network File System, distinguishable by the `nfs` type in the output of the Unix `df` command).

The `filter` keyword, if present, enables texture filtering based on texture pyramids, a technique comparable to mip-map textures. during rendering. Filtered textures are preprocessed before rendering begins and use approximately 30% more memory. Filtering should be used when the texture is large and seen at a distance, such that every sample covers many texture pixels. Without filtering, widely spaced samples ``overlook'' the areas between the samples; filtered textures perform a filter operation to take the skipped areas into account. The compression of the texture on the viewing plane can be scaled by the optional scale value if necessary.

When loading a texture image, it is checked whether the texture is memory-mappable. This is the case if the texture file has the special uncompressed `.map` format. If this is the case, the texture is not loaded into memory but mapped into virtual memory. Memory-mapped textures use far less physical RAM and no swap space, but they use virtual memory. Memory mapping is especially useful for large textures that are not used often (i.e., many or most of its pixels are not sampled or the textured object is small or far away from the camera), but is recommended for all nontrivial texture images. Memory-mapped textures are implicitly also local textures.

Procedural textures are defined by naming a shading function with parameters; the shading function can either be one of the built-in functions or an external function from a `code` or `link` command.

When the material shader (or any other shader) evaluates a texture by calling a texture evaluation function, the program either looks up non-procedural shaders by looking up the texture in the range [0, 1) in each dimension, or it calls the named shader in the procedural case. The shader is free to interpret the point for which it evaluates the texture in any way it wants, two-dimensional or three-dimensional.

## 2.7.4 Materials

        material "material_name"
            [opaque]
            shader_list
            [displace [shader_list]]
            [shadow [shader_list]]
            [volume [shader_list]]
            [environment [shader_list]]
            [contour [shader_list]]
            [photon [shader_list]]
            [photonvol [shader_list]]
        end material

Materials determine the look of geometric objects. They are referenced by material_name in the geometry definition in `object` statements (see below). Lights and textures cannot be referenced by objects; they are referenced by the material which uses them to compute the color of a point on the object's surface. All built-in material shaders accept textures and light instances as shader parameters.

When a primary ray cast from the camera hits an object, that object's material shader (the first, mandatory, shader_list) is called. The material shader then calculates a color (and certain other optional values such as labels, depths, and normals that can be written to special output files). This color may then be modified by the optional volume shader if present. The resulting color is stored in the output frame buffer, which is written to the output picture file when rendering has finished. In order to calculate the color, the material shader may cast secondary reflection, refraction, or transparency rays, which in turn may hit objects and cause other (or the same; multiple objects may share a material) material shaders to be called. The material shader bases the decision whether to cast secondary rays on its parameters, which are part of the scene description and may contain parameters such as the material's diffuse color or its reflectivity and transparency, light instances, and textures. The parameters depend entirely on the material shader. In this sense, material shaders are ``primary'' shaders that get help from ``secondary'' texture and light shaders.

It is possible to specify a shader type such as `shadow` without following it with a shader_list. This is useful if an incremental change is done to the material. The incremental change leaves the contents of the material undisturbed except where explicitly rewritten, so the shadow shader list remains intact. It can be replaced by specifying a new one, but it can only be deleted with a `shadow` keyword not followed by any shaders. In an incremental change, the first statement (say, `volume`) first resets the old volume list; every subsequent `volume` statement in the same material block adds to the list.

The material_name should be quoted to avoid conflicts with reserved names and non-alphabetic characters. The `opaque` flag, if present, informs that this material is not transparent (i.e., it does not cast refraction or transparency rays and always sets its alpha result value to 1); this allows certain optimizations that improve rendering speed. The material shader and its parameters are the only mandatory part of a material.

There are several optional functions that can be listed in a material. The displacement shader is a function returning a scalar that displaces the object's surface in the direction of its normal, or in arbitrary directions. Displacement shaders can be applied to both free-form surface objects and polygonal objects.

The shadow shader is called when a shadow calculation is done, and the shadow ray from the light source towards the point in shadow intersects with this material. The shadow shader then changes the color of the ray, which is initially the (possibly attenuated) color of the light to another color, typically a darker or tinted color if the material is colored glass. It returns black if the material is totally opaque, which is also the default if no shadow shader is present. Shadow shaders are usually reduced versions of the material shaders; they evaluate transparencies and colors but cast no secondary rays. Shadow shaders are only required for transparent objects. If global illumination is enabled, no shadow shaders should be used because global illumination provides a more powerful way to compute light transmission, and using two ``competing'' methods at the same time for the same object may produce incorrect results. This is explained in more detail in the mental ray User's Guide.

It is possible to use the material shader as a shadow shader; material shaders can find out whether they are called as material or shadow shaders and do only the required subset in the latter case. This is done by naming the material shader after the `shadow` keyword, and giving no parameters (i.e., giving `()`). will notice the absence of parameters and pass the material parameters instead. If the shadow shader has no parameters of its own, it is not defined whether it receives a pointer to the material shader parameters, or a pointer to a copy of the material shader parameters.

A volume shader affects rays traveling inside an object. Volume shaders are conceptually similar to fog or atmosphere shaders of other rendering programs. When a ray (either from the eye or from a light source) hits this material, the volume shader, if present, is called to change the color returned by the ray based on the distance the ray has traveled, and atmospheric or material parameters. A volume shader can also be named in the `camera` (see above); that shader is used for rays traveling outside objects. It is the material shader's responsibility to determine inside and outside of objects.

The environment shader is called when a reflection or refraction ray cast by the material shader leaves the scene entirely without striking another object. For example, the environment shader may map a texture on a sphere with an infinite radius surrounding the scene. (This is another example for an application of a texture; a texture name must be used as a parameter for the environment shader for this to work.) The `camera` statement also allows naming an environment shader; that shader is used when the ray leaves the scene without ever striking any object (or exceeding the trace depth).

If a contour shader is given, it is called when contours are enabled with an appropriate output statement in the camera element, and certain contour store and contour contrast shaders are specified in the options element. For more information on contour rendering see chapter .

If caustics or global illumination2.1computation is enabled, the photon shader is called during a preprocessing stage (before rendering) to determine the light distribution in the scene. Like shadow shaders, photon shaders without parameter lists are called with the material shader parameter lists. See the mental ray User's Guide for details.

A volume photon shader affects photons traveling inside an object. When a photon hits this material, the volume photon shader, if present, is called to trace the photon through the volume. Volume photon shaders are to volume shaders what photon shaders are to material shaders.

Materials can be replaced with phenomena. In all places where the name of a material may be given, the name of a shader that references a phenomenon declaration of type `material` is legal. Given the following scene fragment:

         declare phenomenon
              material "phen_mtl" (color "param")
              material "mtl" opaque
                   "shader" ("diffuse" = interface "param")
              end material
              root material "mtl"
         end declare

         shader "mtl_sh" "phen_mtl" ("param" 1.0 0.7 0.3)

the name `mtl_sh` can be used like a material_name, for example in polygon or free-form surface definitions in objects. For more information on material phenomena, see section .

Note that there are three ways to use material shaders in a scene:

- Every polygon and surface in an object specifies a material. They can be omitted but default to the previous polygon or surface in the object, but this is only a syntactical simplification. Effectively, every polygon and surface brings its own material, and no material inheritance takes place.

- If the object is marked `tagged`, polygons and surfaces do not specify materials but integer labels. In this case the inherited material in the instance is used. That material can use mi_query to obtain the label and modify its behavior based on the label.

- As a variation of the previous method, the instance may specify not a single material but a list of materials. In this case, mental ray will use the n-th material in the list if the label of the intersected primitive is n (or the first material if the label is greater than or equal to the number of materials in the list).

See section for more details on material lists and material inheritance.

## 2.7.5 Lights

Lights have a large number of optional parameters that are used if global illumination, caustics or shadow maps are enabled. These techniques use a preprocessing step that analyzes how light travels through the scene. Lights that participate in this preprocessing stage must specify a number of extra parameters. For clarity, regular lights and more specialized lights are shown separately:

        light "light_name"
            shader_list
            [ area_light_primitive ]
            [ origin x y z ]
            [ direction dx dy dz ]
            [ spread spread ]
            [ visible ]
        end light

        light "light_name"
            shader_list
            [ emitter shader_list ]
            [ area_light_primitive ]
            [ origin x y z ]
            [ direction dx dy dz ]
            [ spread spread ]
            [ visible ]
            [ tag labelint ]
            [ energy r g b ]
            [ exponent exp ]
            [ caustic photons storeint [ emitint ]]
            [ globillum photons storeint [ emitint ]]
            [ shadowmap [ on|off ]]
            [ shadowmap resolution resint ]
            [ shadowmap samples numint ]
            [ shadowmap softness size ]
            [ shadowmap file "filename" ]
        end light

This statement defines a light source. All light sources need a light shader, such as the mib_light_point shader in the base shader library, or another shader linked with a `code` or `link` command (see above). `"`shader`"` above stands for the quoted name of the shader. Like any other shader, a parameter list enclosed in parentheses must be given. The parameters depend on the particular shader; they include the light color, attenuations, and spot light directions. The declaration of the shader determines which parameters are available in the parameters list; see chapter for details on shader parameters. distinguishes three kinds of light shaders: point lights, giving off light in all directions; directional (infinite) lights, whose light rays are all parallel in a particular direction, and spot lights which emit light from a point along a certain direction. Point lights must define an `origin` but no `direction`, while directional lights must define a `direction` but no `origin`. Spot lights must define an `origin`, a `direction`, and a `spread`. The spread defines the maximum angle of the cone defined along the direction in which the spot produces illumination. The value of spread is the cosine of this maximum angle; it must be between 0 (infinitely thin) and 1 (hemisphere). Spot lights often use a directional attenuation, but this is purely a function of the shader that is independent of the `spread` and `direction` keywords in the light definition. All types of lights can be turned into area light sources.

After the definition, the light source can be instanced with an `instance` statement that references light_name. The instance can then be referenced in parameter lists of shaders (such as a material shader) by listing the light instance name. Material shaders normally have an array parameter accepting one or more light instances, which they loop over to accumulate the contribution by each light (unless they rely solely on the global light list). Light instances are one of the standard data types that are available for shader parameters. The light_name should be quoted to avoid clashes with predefined words, and to allow non-alphabetic characters.

Any point or spot light may be turned into an area light source by naming an area_light_primitive. Area light sources generate soft shadows because shadow-casting objects may partially obscure the light source. Four types of area light primitives are supported:

        rectangle  [ x0  y0  z0  x1  y1  z1  sampling ]
        disc       [ x  y  z  radius  sampling ]
        sphere     [ radius  sampling ]
        cylinder   [ axis  radius  sampling ]

The common sampling substatement is optional:

        [ u_samples  v_samples  [ level   [ low_u_samples  low_v_samples ]]]

All three area light types are centered at the origin position in the light definition. A rectangular area light is specified by two vectors from the center to two edges; a disc area light is specified by its normal vector and a radius; a sphere area light is specified only by its radius; and a cylinder area light is specified by its axis and radius. Note that the orientation of the rectangle, disc, or cylinder are independent of the direction and any directional attenuation the shader applies, although both will generally be similar. Also note that the end caps of the cylinder are not sampled.

The u_samples and v_samples parameters subdivide the area light source primitive. For discs and spheres, u_samples subdivides the radius and v_samples subdivides the angle. For a cylinder, u_samples subdivides the height and v_samples subdivides the angle. When sampling the area light source, samples one point in each subdivision at a location precisely determined by the sample parameters and a predefined lighting distribution, and then combines the results. The default is 3 for each sample parameter, so an area light source without explicitly given samples parameters is sampled 9 times.

If the optional level exists and is greater than 0, then mental ray will use low_u_samples and low_v_samples instead of u_samples and v_samples, respectively, if the sum of the reflection and refraction trace level exceeds level. The defaults for the low levels are 2. The effect is that reflections and refractions of soft shadows are sampled at lower precision, which can improve performance significantly. Since shaders have control over the trace level in the state, they can influence the switching depth, which can be used to sample soft volume shadows less precisely, for example.

If the rectangle, disc, sphere, or cylinder keyword is specified without any of the following arguments, then the light source reverts to a non-area light source. This is useful for incremental changes.

Light sources are by default invisible. However, area lights can be made visible by adding a `visible` flag to the light. Any `visible` flags on non-area lights are ignored since they have zero size. Light visibility cannot be inherited from the instance.

A label integer can be attached to a light using the `tag` statement. Labels are not used by mental ray in any way, but a shader can use the mi_query function to obtain the label of a light and perform light-specific operations.

The second light form is for caustics and global illumination2.1. It requires specification of the light energy. The light energy is given as an RGB triple to allow colors, but the RGB values are typically much higher than the usual 0...1 range for colors. The number of photons emitted from this light source in the preprocessing step is determined by store, and the number of emitted photons is determined by emit, if specified. When either limit is reached, photon emission stops. If store is 0, emit must be specified and storing is unlimited (this requires mental ray 2.1.37 or later). Physical correctness demands an 1r2 power law for energy falloff, causing the energy received from a light source to fall off with the square of the distance to the light source. However, the `exponent` parameter allows modification of the power law to 1rexp. For any exp other than 2, physical correctness is lost, but for achieving certain looks it is often useful to use exp values between 1 and 2 to reduce the falloff, and better approximate classical local illumination non-physically correct lights.

For caustics, one can specify a caustics photons value that controls the number of caustic photons stored during caustics preprocessing. Similarly, a globillum photons value can be specified for global illumination. Typical values range from 10,000 to 100,000; larger values improve accuracy and reduce blurriness.

Shadow maps are controlled per light source using the information about the light source type and the information provided by the shadow map keywords. Shadow maps are supported for spot lights with a cone-angle less than 90 degrees (i.e. spread > 0), for directional lights, and for point lights. A shadow map is activated for a light source by specifying the `shadowmap` keyword. The resolution of the shadow map which controls the quality and also the amount of memory used is specified with the `shadowmap resolution` keyword, which specifies the width and height of the shadowmap depth buffer in pixels. The `shadowmap softness` and `shadowmap samples` keywords determine the type of shadow produced with the shadow map; if the softness is zero a sharp shadow is generated. If softness is larger than zero, `shadowmap samples` different samples will be taken from the shadowmap, on a square region the size of `shadowmap softness`. This will make the boundaries of the shadows appear softer.

The softness is specified in internal space units on the shadow map projection plane. For directional lights, an orthographic projection is used, so the softness will be constant in the scene, the soft region having roughly the given softness value in size. For other lights, because of the projective projection used, apparent softness will increase with distance from the light. This means that much smaller softness values are usually required for spot lights than directional lights. If an excessively high softness value is specified, a warning will be given during rendering. Very high values tend to blur the shadow out of existence. The number of samples determines the quality of the soft shadow and in general the number of samples should be increased when the softness is increased.

The `shadowmap file` statement can be used to specify a shadow map file in which the shadow map will be saved the first time it is rendered, and subsequently loaded every times it is used. In the case of point lights, six different files will be saved, each for a different direction (the resolution of each file will be lower so that the total number of pixels rendered will be approximately resolution `x` resolution). If objects in the scene move, the old shadow map files should be deleted to prevent loading and re-using outdated shadow maps. If the filename contains the `#` character, it will be expanded by mental ray into a hash code number identifying the transformation of the light instance. This is useful when a light is multiply instanced, because it allows distinguishing between files representing multiple instances of the same light. However, the user must take care to remove obsolete files or they will eventually fill all available disk space.

For spot light sources, the extent of the shadow map is determined by the spread parameter. For directional light sources, the extent of the shadow map is determined by the extent of the parts of the scene that cast shadows. For example, in a scene with small objects on a large background polygon, the small objects casting shadows should have a `shadow` flag, while the background polygon should not. Then the extent of the shadow map will only cover the small objects that cast shadows. If the large background polygon also has the `shadow` flag, the extent of the shadow map will be larger, and the shadow map will lack detail at the small objects where detailed shadows are needed.

## 2.7.6 Objects

All geometry is specified in either camera space or object space, depending on the corresponding statement in the options statement (see section ). In camera space mode, the camera is assumed to sit at the coordinate origin and point down the negative Z axis, and objects are defined using camera space coordinates. In object space mode, the camera location is determined by its instance, and objects are defined in local object coordinates that are positioned in the scene with its object instance. Every object, camera, and light requires an instance.

The appearance of the object, such as color and transparency, is determined by naming materials in the object definition. Before a material can be used in an object, it must be defined. Naming the material determines all aspects of the object's appearance. No further parameters, textures, or lights need to be specified; they are all part of the material definition.

The two most common approaches to materials and objects are to name all materials first and then all objects, which may simplify the implementation of material editors because all materials may be put in a separate file and then included in the `.mi` file using a `$include` command; or materials and objects may be interspersed. Either way, each material definition precedes its first use.

All polygonal and free-form surface objects have the same common format in the `.mi` file:

        object "object_name"
            [ visible   [on|off] ]
            [ shadow    [on|off] ]
            [ trace     [on|off] ]
            [ tagged    [on|off] ]
            [ caustic   [on|off] ]
            [ globillum [on|off] ]
            [ caustic   [mode] ]
            [ globillum [mode] ]
            [ tag label_numberint ]
            [ basis list ]
            group
                [ merge epsilon ]
                vector list
                vertex list
                geometry list
                approximation list
            end group
            ...    # more groups
        end object

The individual parameters are:

- The `object` name object_name serves to uniquely identify the object. The name is not used by in any form except to give meaningful progress reports and error messages. Object names should be enclosed in double quotes to disambiguate them from reserved words.

- The `visible` flag causes the object to be visible. Most objects will have this flag set. Not setting it will make the object invisible to primary rays (those originating from the camera), which means it will disappear from the image. The optional boolean argument defaults to 'on'.

- The `shadow` flag causes the object to cast shadows. The standard case is specifying both the `visible` and `shadow` flags. If an object is very complex, it may be desirable to set only the `visible` flag but not the `shadow` flag, and create a second object that resembles the first one but is much simpler and set the `shadow` but not the `visible` flag on it. The effect is that the object appears unchanged, but shadow calculations see a much simpler shadow object that casts approximately the same shadow as the primary visible object would.

- The `trace` flag serves a similar purpose as the `shadow` flag. Normally, it is always set along with the `visible` and `shadow` flags. It controls whether the object is visible to secondary (reflected or refracted) rays. If the reflecting or refracting objects are fuzzy or only slightly reflective or refractive, it may result in a considerable speedup to make the reflection and refraction rays see a much simpler object than primary rays would. Like with the `shadow` flag, this is achieved by not setting the `trace` flag in the primary, high-definition object, and create a second one that roughly resembles the primary object that has the `trace` flag (and perhaps the `shadow` flag) but not the `visible` flag set.

- The `tagged` flag changes the way geometry is stored. Normally, every polygon, surface, and triangle comes with its own optional material. If an object specifies no materials, the material is inherited from the instance. Objects marked `tagged` do not store materials at all and always rely on the inherited instance material, and permit specifying a non-optional label integer in place of the material in polygon and surface definitions. (Non-optional means that a tagged object must contain one label integer for every polygon and surface.) This label can be accessed by shaders during rendering (i.e. not in displacement or output shaders) using the `miQ_GEO_LABEL` mode of the mi_query function. The idea is that a shared material distinguishes parts of the object by label integer, instead of attaching a different material to each polygon or surface.

- The `caustic` flag2.1 lets the object participate in optimized generation of caustics. A caustic is an illumination effect caused by light that undergoes specular reflections or refractions before it hits a diffuse object. For example a water surface casts irregular light patterns on the floor of a swimming pool. To simulate this effect, the material shader of the floor object must be written to pick up caustic light, and the light source must contain a `caustic photon` statement and contain appropriate photon energy settings. For optimized caustic generation, the options should specify caustic 0 and the water surface and floor objects must have the `caustic` flag set. Refer to the Caustics chapter in this manual for details.

The mode argument controls the caustic operation: 1 enables caustic casting, 2 enables caustic receiving, 3 enables both, and 0 neither. `off` means that the object is invisible to caustic photons, and 'on' is the same as 3. In the pool example, the water surface should have mode 1 and the floor should have mode 2. If the `caustic` keyword is given without mode argument, the mode defaults to `on` (that is, 3). If no `caustic` keyword is given, caustics default to mode 0.

- The `globillum` flag2.1 lets the object participate in optimized generation of global illumination. Global illumination is an illumination effect caused by diffuse interreflection, such as a red table bleeding red color onto an adjacent white wall. To simulate this effect, the material shader of both the table and the wall must specify photon shaders, the wall object material shader must be written to pick up global illumination light, and the light source must contain appropriate photon energy settings. For optimized global illumination simulation, the options should specify globillum 0 and the red table and white wall must have the `globillum` flag set. Refer to the mental ray User's guide for details.

The mode argument controls the global illumination mode: 1 enables global illumination casting, 2 enables global illumination receiving, 3 enables both, and 0 neither. The default is specified by the options. `off` means that the object is invisible to global illumination photons, and `on` (the default) enables global illumination interactions with this object. In the table example, the red table should have (at least) mode 1 and the white wall should have (at least) mode 2. If the `globillum` keyword is given without mode argument, the mode defaults to 3).

If an object is very complex, it may be desirable to set only the `visible` flag but not the `globillum` flag, and create a second object that resembles the first one but is much simpler and set the `globillum` but not the `visible` flag on it. The effect is that the object appears unchanged, but simulation of global illumination is faster since a simpler object is used.

- The `tag` specifies an arbitrary 32-bit number that identifies the object. normally uses the term label, but the keyword `tag` is retained for backwards compatibility. The term tag is used by to identify entries in the scene database; this is of concern only to shader writers. By specifying an appropriate `output` statement in the `camera` (see above), it is possible to cause to write a label file that, for each pixel, contains the label code of the object that the camera ray hits first. Exactly which label is stored is under the control of the material shader; using the label of the foremost object regardless of reflections and refractions is merely the default behavior.

- The basis list is a list of bases to be used in free-form surface descriptions. Only curves and surfaces use bases. For a list of supported bases, see section . The defined bases can be used in all groups that follow, until the end of the object.

- Finally, a list of object groups contains the actual geometric representation. The decision whether to put all geometry into a single object group or to use different groups for different geometric entities is of importance only for free-form surfaces. If two surfaces appear in the same group, they may be connected if the appropriate `connect` statements are used (see below) or if adjacency detection ( edge merging) takes place. Surfaces in different groups cannot be connected. Connecting surfaces means that they will be approximated such that there is no crack between them; they will form one continuous combined surface in the range of the connection. The merge epsilon that can be specified in the group determines the maximum gap between two surfaces that still leads to the automatic connection of both surfaces. The smaller the epsilon, the closer any two surfaces must be to become merged. The results of automatic edge merging depends on a judicious choice of the merge epsilon. By default, the merge epsilon is 0.0, so no edge merging is computed. Generally, it is recommended to use only a single object group in any object and create multiple objects instead because will split multigroup objects into multiple single-group objects internally anyway, and explicit objects allow more control.

At the end of each object group, approximation statements can be given that control the tessellation method. They are valid for both polygonal and free-form surface object groups. In polygonal object groups, the approximation is used only for polygons whose material contains a displacement shader. Free-form surfaces are always controlled by their approximations; see page for details.

The `visible`, `shadow`, `trace`, `caustic`, and `globillum` flags can be overridden by the instance using the standard inheritance mechanism. Instances can specify that a flag in the instanced object is turned on or off, or that it is left unchanged. The object flags are used only if all the instances from the root of the scene DAG down to the object all leave the flag unchanged.

Object groups contain the actual geometry. All geometry needs vector lists and vertex lists. The vector list contains 3D vectors that can describe points in space, normals, texture vertices, basis vectors, motion vectors, and others. Vectors are anonymous, they are triples of floating-point numbers separated by whitespace without inherent meaning. They are numbered beginning with 0. Numbering restarts at 0 whenever a new object group starts.

also accepts a compressed binary format for vectors. Instead of three floating-point numbers, a sequence of 12 bytes enclosed in backquotes is accepted. These 12 bytes are the memory image of three floats in IEEE 854 format, using big-endian byte order. This format is intended for increasing translation and parsing speed when ray is connected to a native translator; it should not be used in files modified with text filters. Many filters and editors refuse to accept files containing binary data, or corrupt them.

Vertices build on vectors. In the `.mi` format, there is no syntactical difference between polygon vertices and control points vertices for free-form surfaces; both are collectively referred to as ``vertices'' in this discussion. All vertices define a point in space and optional vertex normals, motion vectors, derivatives, zero or more textures and basis vectors, and user vectors:

          v    indexint
        [ n    indexint ]
        [ d    indexint indexint [ indexint [ indexint indexint ] ] ]

        [ t    indexint [ indexint indexint ] ]

        [ m    indexint ]
        [ u    indexint
          ...

Polygon vertices may use all of these. Free-form surface control points may use `v` and `m` only; the others are either computed analytically or are specified in other ways as part of the surface definition.

- `v`
  specifies the point in space,

- `n`
  specifies the vertex normal (ignored when the vertex is used as a curve or surface control point),

- `m`
  specifies the motion vector (the distance the point moves during the shutter open time specified in the `options` statement), and

- `t`
  specifies a texture vertex with an optional X/Y basis vector pair for bump map calculation. There can be up to 64 `t` lines for any given `v` vertex. (The texture and basis vectors are ignored when the vertex is used as a curve or surface control point. Texture and basis information for surfaces is defined using a ``texture surface'', described below.)

- `d`
  specifies a first and/or second surface derivative. First derivatives describe the UV parametric gradient of a surface; second derivatives describe the curvature. can compute surface derivatives analytically for free-form surfaces but not for polygons because polygons have no inherent UV coordinate space. Therefore, the `d` keyword must be used to define explicit surface derivatives for polygons. If `d` is followed by two indices they are taken to reference the first derivative dPdu and dPdv (with P being the point in space); if three indices follow they are taken to reference the second derivative d2Pdu2, d2Pdv2, and d2Pdudv; and if five indices follow the first two describe the first derivatives and the next three the second derivatives. Derivatives are not used by , they are made available to shaders only.

- `u`
  specifies a user vector. No constraints are imposed on user vectors. does not operate on them in any way, they are passed through with the vertex and can be picked up by the shader.

Every vertex begins with a `v` statement and ends with the next `v` statement or with the start of the geometry description. All occurrences of index above reference the vector list; 0 is the first vector in this group. References of different types (for example, `v` and `n`) may not reference the same vector. As stated before, all vectors are 3D. If the third coordinate is not used (as is the case for 2D texture vertices, for 2D curve control points, and for 2D surface special points) it should be set to 0.0 by convention. If both the second and third coordinates are unused (as is the case for 1D curve special points), they should both be set to 0.0.

Vertices themselves are numbered independently of vectors. The first vertex in every group is numbered 0. The geometry description is referencing vertices by vertex index, just like vertices are referencing vectors by vector index. This results in a three-stage definition of geometry:

1.
  List of vectors
2.
  List of vertices
3.
  List of geometry

The reason for this three-stage process is that it allows both sharing vectors and sharing vertices. This is best illustrated with an example. Consider two triangles ABC and ABD sharing an edge AB. (This example will use the simplest form of polygon syntax that will be described later in this section.) The simplest definition of this two-triangle object is:

        object "twotri"
            visible
            group
                0.0    0.0    0.0
                1.0    0.0    0.0
                0.0    1.0    0.0
                1.0    0.0    0.0
                1.0    1.0    0.0
                0.0    1.0    0.0

                v 0
                v 1
                v 2
                v 3
                v 4
                v 5

                p "material_name" 0 1 2
                p 3 4 5
            end group
        end object

The first three vectors are used to build the first three vertices, which are used in the first triangle. The remaining three vectors build the next three vertices, which are used for the second triangle. Two vectors are listed twice and can be shared:

        object "twotri"
            visible
            group
                0.0    0.0    0.0
                1.0    0.0    0.0
                0.0    1.0    0.0
                1.0    1.0    0.0

                v 0
                v 1
                v 2
                v 1
                v 3
                v 2

                p "material_name" 0 1 2
                p 3 4 5
            end group
        end object

The order of vector references is noncontiguous to ensure that the second triangle is in counter-clockwise order. Two vertices are redundant and can also be removed by sharing:

        object "twotri"
            visible
            group
                0.0    0.0    0.0
                1.0    0.0    0.0
                0.0    1.0    0.0
                1.0    1.0    0.0

                v 0
                v 1
                v 2
                v 3

                p "material_name" 0 1 2
                p 1 3 2
            end group
        end object

The need for sharing both vectors and vertices can be shown by specifying vertex normals:

        object "twotri"
            visible
            group
                0.0    0.0    0.0
                1.0    0.0    0.0
                0.0    1.0    0.0
                1.0    1.0    0.0
                0.0    0.0    1.0

                v 0    n 4
                v 1    n 4
                v 2    n 4
                v 3    n 4

                p "material_name" 0 1 2
                p 1 3 2
            end group
        end object

In this last example, both vector sharing and vertex sharing takes place. The normal is actually redundant: if no normal is specified, uses the polygon normal. Defaulting to the polygon normal is slightly more efficient than interpolating vertex normals, if vertex normals are explicitly specified.

Two types of geometry can be contained in the geometry list, polygonal geometry and free-from surfaces. In the next sections the syntax of the definitions of polygonal geometry and free-form surfaces is described and illustrated by examples.

An object group permits only one type of geometry, either polygons or surfaces but not both. It is recommended that objects contain only a single object group, so normally objects are either polygonal or surface objects but not both at the same time. Also, vector sharing is supported only for vectors of similar types (point in space, normal, motion, texture, basis vector, derivative, or user vector. A vector may not be referenced by vertices once as a point in space and once as a normal, for example.

## 2.7.7 Polygonal Geometry

Polygonal geometry consists of polygons. For efficiency reasons, distinguishes simple convex polygons from general concave polygons or polygons with holes. Both are distinguished by keyword:

        c  ["material_name"] vertex_ref_list
        cp ["material_name"] vertex_ref_list
        p  ["material_name"] vertex_ref_list
        p  ["material_name"] vertex_ref_list  hole vertex_ref_list ...

If the enclosing object has the `tagged` flag set, mandatory label integers must be given instead of the optional materials:

        c  label_numberint vertex_ref_list
        cp label_numberint vertex_ref_list
        p  label_numberint vertex_ref_list
        p  label_numberint vertex_ref_list  hole vertex_ref_list ...

The `c` keyword selects convex polygons without holes. The results are unpredictable if the polygon is not convex. The `cp` keyword is a synonym for `c` for backwards compatibility; `c` should be used in new translators. The `p` keyword also renders concave polygons correctly, and allows specification of holes, using one or more `hole` keywords, each followed by a vertex_ref_list. If all polygons within the same object group are simple convex polygons containing three sides (i.e. triangles), will pre-process them in a more efficient manner than non-triangular polygons.

A vertex_ref_list is a list of non-negative integers indexthat reference vertices in the vertex list of the group described in the previous section. The first vertex in the vertex list is numbered 0.

Any vertex index can be used in both polygon and hole vertex_ref_lists. A polygon with n vertices is defined by n index values in the vertex list following the material name. The order of the polygon vertices is important. A counter-clockwise ordering of the vertices yields a front-facing polygon. The vertex list of a hole may be ordered either way. Any polygon violating this rule, for example because it has been displaced such that its new normal points the wrong way, causes the error message ``orientation of triangles inconsistent'' and the surface to be dropped.

The material name must have been defined before the object definition that contains the polygon definition, in a statement like

        material "material_name"
            ...
        end material

In both cases, it is recommended to quote the material name to avoid conflicts with reserved words, and to allow arbitrary characters in the name. For a detailed description of material definitions, see section . Once a material name has been specified for a polygon, it becomes the default material. All following polygons may omit the material name. Polygons without explicit material use the same material as the last polygon that does have an explicit material. Not specifying materials improves parsing speed because no names must be looked up in the symbol table.

If no material is specified, polygons remain without material; in this case the material from the closest instance up the scene DAG is used instead. This is called material inheritance. Tagged objects always inherit their material from the instance. It can distinguish polygons by using the `miQ_GEO_LABEL` mode of the mi_query function during rendering (not in displacement shaders).

The tessellation of polygons assumes that polygons are ``reasonably'' planar. This means that every polygon will be tessellated, but the exact subdivision into triangles does not attempt to minimize curvature. If the curvature is low, different tessellations cannot be distinguished, but consider the extreme case where the four corners of a tetrahedron are given as polygon vertices: the resulting polygon will consist of two triangles, but it cannot be predicted which of the four possible triangles will be chosen.

The behavior will be different for convex polygons without holes (`c` keyword) and polygons which contain holes or are concave (`p` keyword). Convex polygons without holes are triangulated by picking a vertex on the outer loop and connecting it with every other vertex except its direct neighbors. If polygons are not flagged with the `c` keyword but do not have any holes an automatic convexity test is performed and if they are indeed convex they are triangulated as described. Convex polygons with holes and concave polygons are triangulated with a different algorithm. In any case a projection plane is chosen such that the extents of the projection of the bounding box of the (outer) loop have maximal size. If the projection of the polygon onto that plane is not one-to-one the results of the triangulation will be erroneous.

If a textured polygon's material contains a displacement map the vertices are shifted along the normals accordingly. If an approximation statement is given triangles are subdivided until the specified criteria are fulfilled; see section for details.

## 2.7.8 Free-Form Surface Geometry

Free-form surfaces are polynomial patches of any degree up to twenty-one.2.5 Supported basis types include Bézier, Taylor, B-spline, cardinal, and basis-matrix form. Any type can be rational or non-rational. Patches can be explicitly or automatically connected to one another, or may be defined to contain explicitly defined points or curves in their approximation. Various approximation types including (regular) parametric, spatial, curvature-dependent, view-dependent, and combinations of these. Surfaces may be bounded by a trimming curve, and may contain holes.

Surface geometry, like polygonal geometry, is defined by a series of sections. An object containing only surface geometry follows this broad outline:

        object "object_name"
            [ visible   [on|off] ]
            [ shadow    [on|off] ]
            [ trace     [on|off] ]
            [ tagged    [on|off] ]
            [ caustic   [on|off] ]
            [ globillum [on|off] ]
            [ caustic   [mode] ]
            [ globillum [mode] ]
            [ tag label_numberint ]
            [ basis list ]
            group
                [ merge epsilon ]
                vector list
                vertex list
                [ list of curves ]
                surface
                [ list of surface derivative requests ]
                [ list of texture or vector surfaces ]
                ... # more surfaces
                [ list of approximation statements ]
                [ list of connection statements ]
            end group
            ... # more groups
        end object

Curves, surfaces, approximations, and connections may be interspersed as long as names are defined before they are used. For example, a curve must come before the surface it is trimming, and an approximation must come after the surface to be approximated. Texture and vector texture surfaces must always directly follow the surface they apply to. The individual sections are:

- The basis list must be specified at the beginning of the object definition, just before the group begins. Bases defined in this section are referenced by name in the curve and surface definitions to specify their degrees and types (Bézier, B-spline, etc.).

- The vector list in the group is a list of (x, y, z) vectors used to build control points later. This section is the same as the vector section used to build vertices for polygonal geometry.

- The vertex list that follows the vector list builds control points out of the vectors. This also works like the vertex list for polygonal geometry, except that no normals and texture vertices can be defined here (i.e., no `n`, `t`, or `d` statements may appear). Normals are defined implicitly by the surface, and textures are defined by texture surfaces instead as described below. Surface derivatives are generated if `derivative` keywords are present. Rational curves and surfaces specify additional weights at each vertex reference (see below).

- Curves may be defined and used as trimming curves, hole curves, and special curves. This section is optional; if no trimming curve is defined surfaces are untrimmed and end at the boundaries specified by the ranges of the bases used. Trimming a surface means to cut away portions that fall outside an outer boundary curve; holes cut away portions inside the hole curve. Special curves are curves that are always included in the tessellation; they can be used to define features like sharp creases that need to be tessellated consistently. Surfaces may also be connected along trimming curves.

- The surface geometry list consists of `surface` statements, much like polygonal geometry that consists of `p` and `c` statements. A surface is defined by a `surface` statement, optionally followed by surface derivative request statements and one or more `texture surface` or `vector surface` statements.

- Approximation statements give additional information about how a surface and its trimming, hole, and special curves are to be approximated with triangles. Various modes such as parametric, regular parametric, curvature-dependent, and view-dependent approximations can be selected, along with the precision. If there are approximation statements in the `options` statement (see Options, Tessellation Quality above), they override any approximation statements in the objects.

For a description of vector lists and vertex lists, refer to page .

### 2.7.8.1 Bases

When surfaces and curves are present within an object group, it is mandatory that at least one basis has been defined within the object. Bases define the degree and type of polynomials (denoted by Ni, n below) to be used in the description of curves or surfaces. Curves and surfaces reference bases by name. Every surface needs two bases, one for the U and one for the V parameter direction. Both can have a different degree, but must have the same type (for example, rational Bézier in U and Cardinal in V is not allowed). There are five basis types:

        basis "basis_name"  [rational]   taylor  degreeint
        basis "basis_name"  [rational]   bezier  degreeint
        basis "basis_name"  [rational]   cardinal
        basis "basis_name"  [rational]   bspline  degreeint
        basis "basis_name"  [rational]   matrix  degreeint   stepsizeint  basis_matrix

A parametric representation may be either non-rational or rational as indicated by the `rational` flag. Rational curves and surfaces specify additional weights at each control point. This flag is optional; it can also be specified in the curves and surfaces that reference the basis.

The degree specifies the degree of the polynomials used in the description of curves or surfaces. Recall that the degree of a polynomial is the highest power of the parameter occurring in its definition. When bases of degree 1 are used control points are connected with straight lines. Cardinal bases always have degree 3. The degree and the type combined determine the length of the parameter vector and the number of control points needed for the surface. The meaning of the parameter vector differs for the different basis types. This is described in detail below.

The supported polynomial types for curves and surfaces are `bezier`, `bspline`, `taylor`, `cardinal` and `matrix`.

`taylor` specifies the basis functions:

Ni, n(t) = ti

`bezier` specifies the basis functions:

`cardinal` specifies third degree curves and surfaces . The Cardinal splines, also known as Catmull-Rom splines, are most easily formulated as a conversion from Bézier form. If we let Bi, 3(t) be the cubic Bézier basis functions (i.e., the above basis functions Ni, n(t) with n = 3), then we may write the cardinal basis functions as

N0, 3 | = | - B1, 3(t) |
N1, 3 | = | B0, 3(t) + B1, 3(t) + B2, 3(t) |
N2, 3 | = | B1, 3(t) + B2, 3(t) + B3, 3(t) |
N3, 3 | = | - B2, 3(t) |

`bspline` specifies a non-uniform B-spline representation whose basis functions are given by the following recursive definition:

Ni, 0(t) =

and

Ni, n(t) = Ni, n - 1(t) + Ni + 1, n - 1(t)

where, by convention, 0/0 = 0. (x0,..., xq) is known as the knot vector. It must be specified through the parameter lists when using B-spline bases in curves and surfaces (see below).

A `matrix` (bi, j)0in, 0jn specifies the basis functions:

Ni, n(t) = bi, jtj

When a curve or surface is being evaluated and a transition from one segment or patch to the next occurs, the set of control points (the `evaluation window') used is incremented by the stepsize. The appropriate stepsize depends on the representation type expressed through the basis matrix and on the degree.

Consider a curve with k control points {v1,..., vk}. If the curve is of degree n, then n + 1 control points are needed for each polynomial segment. If the stepsize is given as s, then the (1 + i)th polynomial segment, will use the control points {vis + 1,..., vis + n + 1}. For example, for Bézier curves s = n, whereas for Cardinal curves s = 1. For surfaces, the above description applies independently to each parametric dimension.

The basis_matrix specifies the basis functions used to evaluate a parametric representation. For a basis of degree n the matrix must be of size (n + 1) `x` (n + 1). The matrix is laid out in the order b0, 0, b0, 1, ... , b0, n, ... , bn, n. Note that the generalization to the rational case for all representations is admitted in all cases.

As an example, an object containing a nonrational Bézier surface of degree 3 in one parameter direction and degree 1 in the other parameter direction needs two bases defined at the beginning of the object like this:

        object "mysurface"
            visible
            basis "bez1" bezier 1
            basis "bez3" bezier 3
            group
                ...

The surface definition will reference the two bases by their names, `bez1` and `bez3`.

### 2.7.8.2 Surfaces

A surface specifies a name and a list of control points. For both parametric dimensions it specifies a basis, a global parameter range, and a parameter list. Optionally, it specifies surface derivative requests, texture surfaces, trimming curves, hole curves, special curves and special points. Special curves and points are included as edges and vertices in the approximation ( triangulation) of the surface.

            surface "surface_name" "material_name"

                "u_basis_name"  range u_param_list
                "v_basis_name"  range v_param_list
                hom_vertex_ref_list
                [ derivative_request ]
                [ texture_surface_list ]
                [ surface_specials_list ]

If the enclosing object has the `tagged` flag set, a label integer must be given instead of a material name (see page ). This changes the first line of the preceding syntax block to:

            surface "surface_name"  label_numberint

The bases used in the definition of the surface must have been defined in the basis list of the object. They are referenced by their basis_names. Their ranges consist of two floating-point numbers specifying the minimum and maximum parameter values used in the respective direction.

The parameter_lists in the basis specifications define the number of patches of the surface and the number of control points. For bases of the types `taylor`, `bezier`, `cardinal` and `matrix` such a parameter_list consists of a strictly increasing list of at least two floating-point numbers. For `bspline` bases the parameter_lists specify the knot vector. If the B-spline basis to be used is of degree n the knot vector (x0,..., xq) must have at least q + 1 = 2(n + 1) elements. Knot values represent a monotone sequence of floating-point numbers but are not necessarily strictly increasing, i.e. xixi + 1. Moreover, they must satisfy the following conditions:

    (1)        x0 < xn + 1
     (2)        xq - n - 1 < xq
     (3)        xi < xi + n    for    0 < i < q-n-1
     (4)        xntmin < tmaxxq - n

where [tmin, tmax] is the range over which the B-spline is to be evaluated. Equation (1) demands that no more than n + 1 parameters at the beginning of the parameter list may have the same value. Equation (2) is the same restriction for the end of the parameter list. Equation (3) says that in the middle of the parameter list, at most nconsecutive parameters may have the same value. To generate closed B-spline curves, it is often necessary to write a parameter list where the first n and last n parameters in the list produce initial and final curve segments that should not become part of the curve; in this case equation (4) allows choosing a start and end parameter in the range bounded by the first and last parameter of the parameter list.

The number of control points per direction can be derived from the number of parameters p, the degree of the basis n, and the step size s. Their total number can be calculated by multiplying the numbers taken from the following table for each of the U and V directions.

`type` | min # of parameters | # of control points
`Taylor` | 2 | (p - 1) . (n + 1)
`Bézier` | 2 | (p - 1) . n + 1
`cardinal` | 2 | p + 2
`basis matrix` | 2 | (p - 2) . s + n + 1
`B-spline` | 2(n + 1) | p - n - 1

Note that only certain numbers of control points are possible; for example, if the U basis is a degree-3 Bézier, the number of control points in the U direction can be 4, 7, 10, 13, and so on, but not 3 or 5. For B-spline bases of degree 3 the minimum number of parameters is 8 corresponding to 4 control points.

Each vertex reference in the hom_vertex_ref_list is an integer index into the vertex list of the current group in the object (index 0 is the first vertex). When the surface is rational, homogeneous coordinates must be given with the control points, by appending a floating-point weight to every vertex reference integer in the hom_vertex_ref_list. There are two methods for specifying weights: either a simple floating-point number that must contain a decimal point to distinguish it from an integer index, or the keyword `w` followed by a weight value that need not contain a decimal point. The `w` keyword method is recommended because it eliminates the requirement that numbers contain decimal points, so translators can use `%g` format specifiers. Weights are used only if the surface is rational and ignored otherwise. If a weight in a rational surface is missing, it defaults to 1.0.

The surface specials list is used to define trimming curves, hole curves, special curves, and special points (vertex references). A surface may be further modified by approximation and connection statements, as described below.

For example, an object with a simple degree-3 Bézier surface can be written as:

         object "mysurface"
              visible
              basis "bez3" bezier 3
              group
                   0.314772   -3.204608  -7.744229   # vector 0
                   0.314772   -2.146943  -6.932366
                   0.314772   -1.089277  -6.120503
                   0.314772   -0.031611  -5.308641
                   -0.660089  -2.650739  -8.465791   # vector 4
                   -0.660089  -1.593073  -7.653928
                   -0.660089  -0.535407  -6.842065
                   -0.660089  0.522259   -6.030203
                   -1.634951  -2.096869  -9.187352   # vector 8
                   -1.634951  -1.039203  -8.375489
                   -1.634951  0.018462   -7.563627
                   -1.634951  1.076128   -6.751764
                   -2.609813  -1.543000  -9.908914   # vector 12
                   -2.609813  -0.485334  -9.097052
                   -2.609813  0.572332   -8.285189
                   -2.609813  1.629998   -7.473326

                   v 0     v 1     v 2     v 3       # vertices
                   v 4     v 5     v 6     v 7
                   v 8     v 9     v 10    v 11
                   v 12    v 13    v 14    v 15

                   surface "surf1" "material"
                           "bez3"  0.0 1.0   0.0 1.0
                           "bez3"  0.0 1.0   0.0 1.0
                           0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
              end group
         end object

First, 16 vectors are defined, each of which is used to build one vertex (control point). Next, a surface is defined that uses basis `bez3` for both the U and V parameter directions. Since the surface is built from only one 4 `x` 4 Bézier patch, the parameter vector after the basis range has only length 2. If there had been two patches in the U direction and three in the V direction, the bases would have been referenced as

                           "bez3"  0.0 1.0 0.0 0.5 1.0
                           "bez3"  0.0 1.0 0.0 0.33333 0.66667 1.0

Alternatively, the parameter vector may be given as

                           "bez3"  0.0 2.0 0.0 1.0 2.0
                           "bez3"  0.0 3.0 0.0 1.0 2.0 3.0

by changing the parameter range of the basis. This has no influence on the geometry of the surface, but generates UV texture coordinates in a different range (here, [0.0, 2.0] `x` [0.0, 3.0]). However, a different parametrization does affect the texture surface range (see below), and the range of trimming, hole, and special curves (which do not define their own ranges but borrow the range from the surface they apply to).

The optional surface_specials_list that completes the surface definition is a sequence of trimming curves, hole curves, special curves, and special points as described in the next section.

### 2.7.8.3 Surface Derivatives

can automatically generate surface derivative vectors if requested. First derivatives describe the UV parametric gradient of a surface; second derivatives describe the curvature. They are computed and stored only if requested by derivative_request statements in the surface definition:

        derivative  numberint  [numberint]

There can be one or more `derivative` statements that request first and/or second derivatives. Valid values for number are 1 and 2, for first and second derivatives, respectively.

does not use derivative vectors but makes them available to shaders. First derivatives are presented as two vectors (dPduand dPdv, with P being the point in space); second derivatives are presented as three vectors (d2Pdu2, d2Pdv2, and d2Pdudv). This is the same format that can be explicitly given for polygonal data using the `d` keyword in vertices. Surfaces always compute the vertex derivatives analytically, explicit vertex derivatives given by `d` keywords are ignored.

### 2.7.8.4 Texture Surfaces

A plain `surface` statement defines the geometry of the surface. If a texture is to be mapped on the surface, it is necessary to include texture surfaces. A texture surface defines a mapping from raw UV coordinates to texture coordinates as used by shaders. A vector texture is a variation of a texture surface that additionally defines a pair of basis vectors; it is used for bump mapping.

The texture or vector texture directly following a surface defines texture space number 0, the next defines texture space number 1, and so on, exactly like the first `t` statement after the `v` statement in a vertex used for building polygonal geometry defines texture space number 0, the next `t` defines texture space number 1, and so on. Basically, texture and vector texture surfaces replace the `t` statements used by polygonal geometry, because attaching textures to control points that usually are not part of the surface is not useful.

Texture spaces is what ends up in the state - > tex_listarray where it can be accessed by texture shaders to decide which texture is mapped which way. Texture space 0 is the first entry in that array, which is used by the shader for the first texture listed in the texture list in the material definition. In general, there is one texture space per texture on a material, although shaders making nonstandard use of texture spaces could be written.

The syntax for texture surfaces is a simplified version of geometric surfaces. The texture_surface_list in the grammar summary at the beginning of the ``Surfaces'' section above expands to zero or more copies of the following block:

        [ volume ] [ vector ] texture
            "u_basis_name" u_param_list
            "v_basis_name" v_param_list
            vertex_ref_list

Unlike geometric surfaces, no surface name and material name is given. Bases are given like in geometric surfaces. Texture surfaces use the ranges of the geometric surface they are attached to, they are not repeated in the texture surface basis statements. The vertex_ref_list follows the same rules as the geometric surface's vertex_ref_list. Texture surfaces have no specials such as trimming curves or holes.

The optional `volume` keyword in the texture surface definition disables seam compensation. It should be used for 3D textures where each texture vector should be used verbatim. If the `volume` flag is missing, the tessellator detects textures that span the geometric seam on closed surfaces, and prevents rewinding. Consider a sphere with a 2D texture that is shifted slightly in the U parameter direction: a triangle might have u0 = 0.0 on one side and u1 = 0.1 on the other side. If the texture is shifted towards higher u coordinates by 0.05, u0 and u1 will map to texture coordinates t0 = 0.95and t1 = 0.05, assuming an otherwise normal UV mapping. Even though u0 < u1, t0 > > t1, causing a fast ``rewind'' of the texture. Seam compensation corrects t1 to 1.05. This is undesirable for 3D textures, which should have the `volume` keyword set. Most problems with strangely shifted textures are caused by inappropriately used or missing `volume` keywords.

The optional `vector` keyword in the texture surface definition is a flag that causes bump basis vectors to be calculated during tessellation. This flag must be used if the texture surface is used for a bump map; all built-in shaders supporting bump maps expect such a pair of bump basis vectors.

For a geometric surface S that maps parameters (u, v) into an object's coordinates (x, y, z) and a texture surface T that maps the same parameters into texture coordinates (s, t), the bump map basis vectors are the derivatives

(S`o`T-1)/s(S`o`T-1)/t

of the composite map S`o`T-1 from the texture coordinates into object coordinates. They are not normalized and not necessarily orthogonal to each other.

The normal perturbation as suggested by Blinn (see [Watt 92] sec. 6.4, pp. 199-201) is given by

lclD | = | M' - M |
| = | (H/s)A - (H/t)B |

with

lclA | = | N `x` (S`o`T-1)/t |
B | = | N `x` (S`o`T-1)/s |

where

N = M/M

is the normalized surface normal with

M = (S`o`T-1)/s `x` (S`o`T-1)/t

and H a height field defining the bump map, usually the intensity of the picture stored in the texture.

This is an example for the simplest of all texture surfaces, a bilinear mapping:

         object "mysurface"
             visible
             basis "bez1" bezier 1
             basis "bez3" bezier 3
             group

                 # ... 16 vectors used for the surface
                 0.0  0.0  0.0       # vector number 16
                 0.0  1.0  0.0       # vector number 17
                 1.0  0.0  0.0       # vector number 18
                 1.0  1.0  0.0       # vector number 19

                 # ... 16 vertices used for the surface
                 v 16                # vertex number 16
                 v 17                # vertex number 17
                 v 18                # vertex number 18
                 v 19                # vertex number 19

                 surface "surf1" "material"
                     "bez3"    0.0 1.0    0.0 1.0
                     "bez3"    0.0 1.0    0.0 1.0
                     0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

                 texture
                     "bez1"    0.0 1.0
                     "bez1"    0.0 1.0
                     16 17 18 19
             end group
         end object

This texture surface defines a bilinear mapping from the UV coordinates computed during surface tessellation to the texture coordinates. To define other than bilinear mappings, the texture surface needs to have more control points than just one at every corner of the surface. Whenever the surface tessellator generates a triangle vertex, it uses the UV coordinate of that vertex to look up the texture surface and interpolate the texture coordinate from the nearest four points of the texture surface. The resulting texture coordinate is stored with the vertex and becomes available in state - > tex_list when the material shader is called because a ray has hit the surface.

If more than one texture surface is given, one texture coordinate is computed for each texture surface and stored in sequence in the generated triangle vertices. Each texture surface is said to define a `` texture space''. They are available in the state - > tex_list array in the same order. The number and order of texture surfaces should agree with the number and order of textures given in the texture list in the material definition. (Note that not all material shaders support multiple textures.)

If the material name of a surface is empty (two consecutive double quotes), the surface uses the material from the closest instance (this is called material inheritance).

### 2.7.8.5 Curves

Curves are two-dimensional parametric curves when they are referenced by surfaces. They are used as trimming curves, hole curves, and special curves. They must be defined before the surface which references them. Curves are three-dimensional parametric curves when referenced by space curves. A curve is defined as:

            curve "curve_name" "basis_name"
                parameter_list
                hom_vertex_ref_list
                [ special  special_point_list ]

The parameter_list of a curve is a list of monotonically increasing floating-point numbers that define the number of segments of the curve and the number of control points. Curve parameter lists work very much the same way as surface parameter lists except that no range needs to be provided, because they are supplied by the surfaces that reference the curve under consideration as explained in the next section. For details on parameter lists, see the sections on bases and surfaces above.

Each vertex reference in the hom_vertex_ref_list is an integer index into the vertex list of the current group in the object (index 0 is the first vertex), optionally followed by the keyword `w` and a weight value. (For backwards compatibility, the `w` keyword may be omitted if the weight is a floating-point value containing a decimal point.) Weights are used only if the curve is rational, they are ignored otherwise. If a weight in a rational curve is missing, it defaults to 1.0. The vertices indexed by the integers in the hom_vertex_ref_list should have no normals or textures (no `n` and `t` statements), and the third component of the vector (`v` statement) should be 0.0 because curves are defined in UV space, not 3D space.

The optional special_point_list specifies points that are included in the approximation of the curve. After the `special` keyword, a sequence of integers follows that index into the vertex list, just like the integers in the hom_vertex_ref_list. The first component of the vector is used as the t parameter; it forces the point on the curve at parameter value t to become part of the curve approximation. Of course t must be in the range of parameters allowed by the surface definition.

### 2.7.8.6 Trimming, Hole, and Special Curves; Special Points

A surface may reference curves to trim the surface, to cut holes into it, and to specify `` special curves'' that become part of the tessellation of the surface. Special points in surfaces work like special points in curves, except that they provide a point in the parameter range of the surface, that is, a two-dimensional UV coordinate, rather than a one-dimensional curve parameter. They specify single points on the surface that are to be included in the tessellation. As all curves and points are in UV space, the third component of the vectors provided for them is ignored. None of the above types of curves and points may exceed the range of (0.0, 1.0) at any point.

No two curves may intersect each other, and no curve may self-intersect. This is an important point because trimming curves and holes that are not closing or intersecting themselves or other loops can produce unexpected tessellation results.

Trimming, hole, and special curves and special points are defined at the end of the surface definition. The curves are composed of segments from the list of curves of the surface's group. The surface_specials_list given in the previous section is a list of zero or more of the following four items:

        trim    "curve_name"  min  max
            ...
        hole    "curve_name"  min  max
            ...
        special    "curve_name"  min  max
            ...
        special    vertexint
            ...

The dots indicate that each trim, hole, and special statement may be followed by more than one curve segment or vertex, respectively. All listed segments are concatenated to form a single curve.

The vertex integers specify vertices from the vertex section of the current group in the current object. Such a vertex specifies the UV coordinate of the special point that is to be included in the tessellation.

Each of the three types of curves references a curve that has been defined earlier with a `curve` statement. If a single `trim`, `hole`, or `special` statement is followed by more than one curve, the resulting trimming, hole, or special curve is pieced together by concatenating the given curves. The min and max parameters allow using only part of the curve referenced. min and max must be in the range of the parameter vector of the curve which in turn must be mapped into the parameter range of the surface. The min and max parameters of two different curve pieces are independent, they only depend on the curve parameter lists. For example, a trimming curve can be built from two curves, using the first three quarters of the first curve and the last three quarters of the second curve:

        curve "trim1"
                "bez1" 0.0 1.0 2.0 3.0 4.0
                0 1 2 3 4

        curve "trim2"
                "bez1" 0.0 1.0 2.0
                3 5 0

        surface "patch1" "mtl"
                "bez3" 0.0 1.0        0.0 1.0
                "bez3" 0.0 1.0        0.0 1.0
                6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
                trim "trim1" 0.0 3.0
                     "trim2" 0.5 2.0

Both trimming curves use the basis `bez1`, which is assumed to be a degree-1 linear curve. Hence, `trim1` connects the UV vertices 0, 1, 2, 3, and 4 with straight lines, and `trim2` connects the vertices 3, 5, and 0. If these two curves are put together by the `trim` statement in the surface definition, all parts of the surface that fall outside the polygon formed by the UV vertices 0, 1, 2, 3, and 5 are trimmed off. The `trim2` curve includes vertex 0 to close the trimming curve. Holes and special curves are constructed exactly the same way. Trimming curves and holes must form closed loops but special curves are not restricted in this way.

Note that trimming and hole curves must be listed in the correct order, outside in. If there is an outer trimming curve, it must be listed first, followed by the holes. If a hole has a hole, the inner hole must be listed after the outer hole. Since curves may never intersect, there is always an unambiguous order - if a curve A encloses curve B, A must be listed before B. Curves that do not enclose one another can be listed in any order.

This example omits the vector and vertex parts of the group in the object. Here is an example that defines a complete object containing a surface with a trimming curve that precisely follows the outer boundary. A trimming curve that follows the outer surface boundary does not actually clip off any part of the surface, but it is still useful if surfaces are to be connected, because connections work on trimming curves.

         object "mysurface"
             visible
             basis "bez1" bezier 1
             basis "bez3" bezier 3
             group

                 # ... 16 vectors used for the surface
                 0.0  0.0  0.0    # vector number 16
                 1.0  0.0  0.0    # vector number 17
                 1.0  1.0  0.0    # vector number 18
                 0.0  1.0  0.0    # vector number 19

                 # ... 16 vertices used for the surface
                 v 16             # vertex number 16
                 v 17             # vertex number 17
                 v 18             # vertex number 18
                 v 19             # vertex number 19

                 curve "trim1"
                     "bez1" 0.0  0.25  0.5  0.75  1.0
                     16  17  18  19  16

                 surface "surf1" "material"
                     ...
                     trim "trim1"  0.0  1.0
             end group
         end object

The trimming curve in the example is linear, using a degree-1 Bézier basis. This means that the parameter vector has five equally-spaced parameters, one for each corner in counter-clockwise order and back to the first corner to close the trimming curve. Trimming and holes always require a closed curve or sequence of curves (they can be pieced together by multiple curves as long as the pieces form a closed loop together). The results are undefined if trimming or hole loops are not closed, or intersect.

If the trimming curve would be a degree-3 Bézier going through four corner points, a parameter vector with 3 . 5 + 1 = 16 parameters would be required (again, the 5 is the number of corners visited including the return to the first to close the curve).

For details on the parameter vector following the basis name in the definition of the curve, refer to section . The bases and parameter vectors for curves and surfaces follow the same rules, except that curves have no explicit range; they always use the implicit range given by the parameter list.

### 2.7.8.7 Space Curve Geometry

Unlike trimming curves, space curves2.1are defined in 3D space. A space curve object may not contain any other type of geometry, such as free-form surfaces or polygons. Space curves are not rendered but serve as input geometry for modeling operations, by passing the space curve object as a parameter to a geometry shader. The curve geometry is defined as a list of space curves , each referencing multiple curve segments.

An object containing space curve geometry follows this outline:

        object "object_name"
            [ tag  label_numberint ]
            [ basis list ]
            group
                [ merge  epsilon ]
                vector list
                vertex list
                [ list of curves ]
                space curve
                [ list of curve segment references ]
            end group
            ...    # more groups
        end object

A single space curve definition follows this outline:

        space curve    "curve_name"  min  max
            ...

The dots indicate that each space curve statement may be followed by more than one curve segment reference. The min and max parameters allow using only part of the curve referenced. min and max must be in the range of the parameter vector of the curve.

Here is an example of a space curve object:

         object "myspacecurve"
             basis "bezier_1" bezier 1
             group
                 0.4 0.4 1.2
                 0.6 0.4 1.2
                 0.6 0.6 1.2
                 0.4 0.6 1.2
                 v 0 v 1 v 2 v 3
                 curve "curve1" bezier_1
                        0. 1. 2. 3. 4.
                        0 1 2 3 0
                 space curve "sp1"
                        "curve1" 0. 4.
             end group
         end object

### 2.7.8.8 Approximations

Approximations are defined within an object group and they specify how previously defined polygons, surfaces and curves should be tessellated. Within an object group containing free-form surface geometry the approximation statements are given separately for the surface itself and for curves used by the surface. The `surface` approximation statement sets the approximation technique for the surface itself. If it carries a displacement map this statement refers to the underlying geometric base surface and does not take the displacement into account. One may specify the approximation criteria on the displaced surface with an additional `displace` approximation statement or even leave out the `surface` approximation statement altogether.

If the material of the surface does not contain a displacement shader the `displace` approximation statement is ignored. A `trim` approximation statement applies to all trimming, hole and special curves attached to the given surface or surfaces collectively; it is equivalent to separate `curve` approximations for each individual curve. When the keyword `approximate` is directly followed by an approximation technique it refers to a polygon or a list of polygons. It only has an effect on displacement mapped polygons. If the `options` statement specifies approximation statements for base surfaces and/or displacements, they override the approximation statements in the object. This can be used for quick previews with low tessellation quality, for example.

        approximate
            technique [ minint  maxint ]
        approximate surface
            technique [ minint maxint ] [ max maxint ] "surface_name" ...

        approximate displace
            technique [ minint  maxint ] "surface_name" ...

        approximate trim
            technique [ minint  maxint ] "surface_name" ...

        approximate curve
            technique [ minint  maxint ] "curve_name" ...

        approximate space curve
            technique [ minint  maxint ] "spacecurve_name" ...

The dots indicate that there may be more than one surface_name or curve_name following the approximation statement. The given approximation is then used for all named surfaces or curves.

technique stands for one or more of the following:

        view
        tree
        grid
        delaunay
        [ regular ]  parametric  u_subdiv  [ v_subdiv ]

        any
        length     edge
        distance   dist
        angle      angle
        spatial    [ view ]  edge
        curvature  [ view ]  dist  angle
        grading    angle

`tree`, `grid`, and `delaunay`2.1are mutually exclusive. `parametric` cannot be combined with any of the others except `grid`, which is the default for the parametric case anyway. `regular` can only be used together with `parametric`. `view` has no effect unless one of `length`, `distance`, `spatial`, or `curvature` is also given. Grading can only be used in combination with Delaunay triangulation.

View-dependent approximation is enabled if the `view` statement is present. It controls whether the edge argument of the `length` and `spatial` statements, and the `dist` argument of the `distance` and `curvature` statements, are in the space the object is defined in or in raster space.

Tree, grid, and Delaunay approximation algorithms are available for surface approximation. The grid algorithm tessellates on a regular grid of isolines in parameter space; the tree algorithm tessellates in a hierarchy of successive refinements that produces fewer triangles for the same quality criteria; the Delaunay algorithm creates a successive refinement that maximizes triangle equiangularity. criteria. By definition parametric approximations always use the grid algorithm; all others can use either but `tree` is the default. `tree`, `grid`, and `delaunay` have no effect on curve approximations. Delaunay triangulation creates more regular triangles but takes longer to compute.

Parametric approximation subdivides each patch of the surface into u_subdiv . degree equal-sized pieces in the U parameter direction, and v_subdiv . degree equal-sized pieces in the V parameter direction. If `regular` the number of pieces the whole surface is subdivided into simply equals the parameter value. v_subdivmust be present for `surface` approximations and must be omitted for `curve` and `trim` approximations. Note that the factor is a floating point number, although a patch can only be subdivided an integral number of times. For example, if a factor of 2.0 is given and the surface is of degree three, each patch will be subdivided six times in each parametric direction. If a factor of 0.0 is given, each patch is approximated by two triangles.

Curves are subdivided in subdiv . degree equal pieces by the `parametric` approximation and into subdiv equal pieces by the `regular parametric` approximation.

For displacement mapped polygons and displacement mapped surfaces with a `displace` statement `regular parametric` has the same meaning as `parametric` in the approximation. For displacement mapped polygons the u_subdiv constant specifies that each edge in the triangulation of the original polygon is subdivided for the displacement 2u_subdivtimes. If a `displace` approximation is given for a displacement mapped surface, the initial tessellation of the underlying geometric surface is subdivided in the same way as for polygons. For example, a value of 2 leads to a fourfold subdivision of each edge. Non-integer values for the subdivision constant are admissible. Nothing is done if the expression above is smaller than 2 (i.e. if u_subdiv < 1). The v_subdiv constant is ignored for the parametric approximation of displacement maps.

Length/distance/angle (LDA) approximation specifies curvature-dependent approximation according to the criteria specified by the `length`, `distance`, and `angle` statements. These statements can be given in any combination and order, but cannot be combined with parametric approximation in the same `approximate` statement. If they are preceded by the `any` keyword2.1the approximation stops as soon as any of the criteria is satisfied.

The `length` statement subdivides the surface or curve such that no edge length of the tessellation exceeds the edge parameter. edge is given as a distance in the space the object is defined in, or as a fraction of a pixel diagonal in raster space if the `view` keyword is present. Small values such as 1.0 are recommended. For tree and grid approximation the min and max parameters, if present, specify the minimum and maximum number of recursion levels of the adaptive subdivision. The min parameter is a means to enforce a minimal triangulation fineness without any tests. Edges are further subdivided until they satisfy the given criterion is fulfilled or the max subdivision level is reached. The defaults are 0 and 5, respectively; 5 is a very high number. Good results can often be achieved with a maximum of 3 subdivisions. For Delaunay approximation, the number max following the keyword `max` specifies the maximum number of triangles of the surface tessellation. This number will be exceeded only if required by trimming, hole, and special curves because every curve vertex must become part of the tessellation regardless of the specified maximum.

For displacement mapped polygons and displacement mapped surfaces with a `displace` approximation statement the length criterion in the approximation limits the size of the edges of the displaced triangles and ensures that at least all features of this size are resolved. Subdivision stops as soon as an edge satisfies the criterion or when the maximum subdivision level is reached. The possibility that at an even finer scale new details may show up which would lead again to longer edges of course cannot be ruled out. This caveat about the potential miss of high-frequency detail applies also to the distance and angle criteria.

The `distance` statement specifies the maximum distance dist between the tessellation and the actual curve or surface. The value of dist is a distance in the space the object is defined in, or a fraction of a pixel diagonal in raster space if the `view` statement is present. As a starting point, a small distance such as 0.1 is recommended. For tree and grid approximation the min and max parameters, if present, specify the minimum and maximum number of recursion levels of the adaptive subdivision. For Delaunay approximation, the number max following the keyword `max` specifies the maximum number of triangles of the surface tessellation.

For displacement mapped polygons and displacement mapped surfaces with a `displace` approximation statement the distance criterion cannot be used in the same way because the displaced surface is not known analytically. Instead, the displacements of the vertices of a triangle in the tessellation are compared. The criterion is fulfilled only if they differ by less than the given threshold. Subdivision is finest in areas where the displacement changes. For example, if a black-and-white picture is used for the displacement map the triangulation will be finest along the borders between black and white areas but the resolution will be lower away from them in the uniformly colored areas. In such a case one could choose a moderately dense parametric `surface` approximation that samples the displacement map at sufficient density to catch small features, and use the curvature-dependent `displace` approximation to resolve the curvature introduced by the displacement map. Even if the base surface is triangulated without adding interior points, as if its trim curve defined a polygon in parameter space, it is still possible to guarantee a certain resolution by increasing the min subdivision level. Only the consecutive subdivisions are then performed adaptively.

The `angle` statement specifies the maximum angle angle in degrees between normals of adjacent tiles of a displaced polygon or the tessellation of a surface or its displacement or between tangents of adjacent segments of the curve approximation. Large angles such as 45.0 are recommended. For tree and grid approximation the min and max parameters, if present, specify the minimum and maximum number of recursion levels of the adaptive subdivision. For Delaunay approximation, the number max following the keyword `max` specifies the maximum number of triangles of the surface tessellation.

Spatial approximation as specified by a `spatial` statement is a special case of an LDA approximation that specifies only the `length` statement. For backwards compatibility, the `spatial` statement has been retained; it is equivalent to the `length` statement plus an optional `view` statement.

Curvature-dependent approximation as specified by the `curvature` statement is also a special case of LDA approximation, equivalent to a `distance` statement, an `angle` statement, and an optional `view` statement. The `spatial` and `curvature` statements can be combined, but future designs should use `length`, `distance`, and `angle` directly.

Grading applies only to Delaunay triangulation2.1controls the density of triangles around the border of the surface. It allows the density of triangles to vary quickly in a smooth transition between a finer curve approximation and a coarser surface approximation. The angle constant specifies a lower bound related to the degree of the minimum angle of a triangle. Values from 0.0 to 30.0 can be specified. Small values up to 20.0 are recommended. The default is 0.0. When using high grading values it is recommended to specify a maximum number of triangles because otherwise high grading values might result in a huge number of triangles or endless mesh refinement. The purpose of this option is to prevent a large number of tiny triangles at the trimming or hole curve to abruptly join very large triangles in the interior of the surface.

If no approximation statement is given the parametric technique is used by default with u_subdiv = v_subdiv = 1 for surfaces, or u_subdiv = 1 in the case of curves and u_subdiv = 0 for polygons.

### 2.7.8.9 Connections

Connections may be defined within a group to specify the connection between two surfaces along intervals of their respective trimming curves or hole curves. They may be used in place of or in addition to the edge merging performed on the group level. A connection is defined as:

        connect  "surface_name1"  "curve_name1"  min1  max1
                 "surface_name2"  "curve_name2"  min2  max2

This statement connects two surfaces surface_name1 and surface_name2 by connecting their trimming curves curve_name1and curve_name2. The curves are connected only in the range (min1...max1) and (min2...max2), respectively. They share the same points, but normals, textures etc. are evaluated on the individual surfaces. Only surfaces that have trimming curves can be connected by an explicit connect statement; for an example for a simple trimming curve that goes around the edge of a surface see the section on curves above. Trimming curves used in connections must satisfy three conditions:

- As always, the trimming curve or sequence of trimming curves must be closed.

- It does not matter whether the trimming curve is oriented clockwise or counterclockwise, but if a sequence of trimming curves is used all pieces must have the same direction.

- The trimming curves along the connected range must run in the same direction in 3D space.

The range values min1, 2 and max1, 2 must not exceed the range of the trimming curve segment as referenced by a `trim` statement of the corresponding surface. The minimum value must be less than the maximum value; it is not possible to satisfy the third condition by inverting the range.

Best results are obtained if the curves to be connected are close to each other in world space and have at least approximately the same length. `connect` is not meant to be a replacement for proper modeling. For carefully modeled surfaces it will not be necessary most of the time. Its purpose is to close small cracks between adjacent surfaces that are already not too far from each other. Topologically complex situations with several connections meeting in a point are beyond its scope.

### 2.7.8.10 Example

Here is an example of two surfaces that meet along one of their edges such that a gap remains. A connection is used to close the gap. The four control points defining the straight trimming curves that are connected are marked as #0, #1, #2, and #3; the control points of the second surface marked `(*)` have been modified slightly to create the gap. This is a complete .mi file that can be rendered directly.

        verbose on
        link "base.so"
        $include <base.mi>

        options "opt"
            samples      -1 1
            contrast     .1 .1 .1 .1
            trace depth  2 2
        end options

        camera "cam"
             frame      1
             output     "rgb" "x.rgb"
             focal      50.000000
             aperture   44.724029
             aspect     1.179245
             resolution 500 424
        end camera

        instance "cam_inst" "cam" end instance

        light "light"
            "mib_light_point" (
                "color"  1 1 1,
                "shadow" on,
                "factor" 1
            )
             origin      140.189178 83.103180 50.617714
        end light

        instance "light_inst" "light" end instance

        material "mtl" opaque
            "mib_illum_phong" (
                "ambience"  .3 .3 .3,
                "ambient"   .5 .5 .5,
                "diffuse"   .7 .7 .7,
                "specular"  1 1 1,
                "exponent"  50,
                "lights"    [ "light_inst" ]
            )
        end material

        object "obj"
            visible shadow trace

            basis "bez1" bezier 1
            basis "bez3" bezier 3
            group "example"
                0.314772    -3.204608   -7.744229
                0.314772    -2.146943   -6.932366
                0.314772    -1.089277   -6.120503
                0.314772    -0.031611   -5.308641    #0
                -0.660089   -2.650739   -8.465791
                -0.660089   -1.593073   -7.653928
                -0.660089   -0.535407   -6.842065
                -0.660089   0.522259    -6.030203    #1
                -1.634951   -2.096869   -9.187352
                -1.634951   -1.039203   -8.375489
                -1.634951   0.018462    -7.563627
                -1.634951   1.076128    -6.751764    #2
                -2.609813   -1.543000   -9.908914
                -2.609813   -0.485334   -9.097052
                -2.609813   0.572332    -8.285189
                -2.609813   1.629998    -7.473326    #3

                0.000000    0.000000    -5.000000    #0 (*)
                1.224400    0.561979    -6.081950
                2.134028    1.155570    -6.855258
                3.043655    1.749160    -7.628566
                -0.500000   0.700000    -6.000000    #1 (*)
                0.249538    1.115849    -6.803511
                1.159166    1.709439    -7.576819
                2.068794    2.303029    -8.350128
                -1.200000   1.000000    -7.000000    #2 (*)
                -0.725323   1.669719    -7.525073
                0.184305    2.263309    -8.298381
                1.093932    2.856899    -9.071690
                -2.000000   2.000000    -7.500000    #3 (*)
                -1.700185   2.223588    -8.246634
                -0.790557   2.817178    -9.019943
                0.119071    3.410769    -9.793251

                0.0     0.0     0.0
                1.0     0.0     0.0
                1.0     1.0     0.0
                0.0     1.0     0.0

                v 0  v 1  v 2  v 3  v 4  v 5  v 6  v 7
                v 8  v 9  v 10 v 11 v 12 v 13 v 14 v 15

                v 16 v 17 v 18 v 19 v 20 v 21 v 22 v 23
                v 24 v 25 v 26 v 27 v 28 v 29 v 30 v 31

                v 32 v 33 v 34 v 35

                curve "curve1"
                     "bez1" 0.0 0.25 0.5 0.75 1.0
                     32 33 34 35 32

                curve "curve2"
                     "bez1" 0.0 0.25 0.5 0.75 1.0
                     32 35 34 33 32

                surface "patch1" "mtl"
                     "bez3" 0.0 1.0        0.0 1.0
                     "bez3" 0.0 1.0        0.0 1.0
                     0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
                     trim "curve1" 0.0 1.0

                surface "patch2" "mtl"
                     "bez3" 0.0 1.0        0.0 1.0
                     "bez3" 0.0 1.0        0.0 1.0
                     16 17 18 19 20 21 22 23
                     24 25 26 27 28 29 30 31
                     trim "curve2" 0.0 1.0

                approximate surface parametric 1.0 1.0 "patch1"
                approximate surface parametric 1.0 1.0 "patch2"
                approximate trim    parametric 3.0     "patch1"
                approximate trim    parametric 3.0     "patch2"

                connect "patch1" "curve1" 0.25 0.5
                        "patch2" "curve2" 0.0  0.25
            end group
        end object

        instance "obj_inst"   "obj"   end instance

        instgroup "root"
            "light_inst" "cam_inst" "obj_inst"
        end instgroup

        render "root" "cam_inst" "opt"

Note that the trimming curves `curve1` and `curve2` have a different orientation, one clockwise and one counterclockwise, because their control point lists are in a different order. This means that where both trimming curves run in parallel, they run in the same direction in 3D space, which is a required condition for trimming curves to be connected. The trimming curves must be closed (another condition) and so run around all four edges of the (square) surfaces. Since only one edge of each surface is connected to the other, the connection ranges select only one quarter (0.5...0.25 and 0.25...0.0) of each curve.

The example produces the following image, once rendered without and then with the `connect` statement:

## 2.7.9 Instances

        instance "name"
            "element"|geometry  function

            [ hide              on|off ]
            [ visible           on|off ]
            [ shadow            on|off ]
            [ trace             on|off ]
            [ caustic           [ mode ]]
            [ globillum         [ mode ]]
            [ transform         [ matrix ]]
            [ motion transform  [ matrix ]]
            [ motion            off ]
            [ material          "material_name" ]
            [ material          [ "material_name" [ , "material_name" ... ] ] ]
            [ (parameters) ]
        end instance

Instances place cameras, lights, objects, and instance groups into the scene. Without instances, these entities have no effect; they are not tessellated and are not scheduled for processing. An instance has a name that identifies the instance when it is placed into an instance group (see below). Every instance references exactly one element element, which must be the name of a camera, a light, an object, or an instance group. If the instanced item is a geometry shader function, the scene element created by this special shader is actually used as the instanced item.

The `hide` flag can be set to `on` to disable the instance and the element it references. This is useful to temporarily suspend an instance to evaluate a subset of the scene, without deleting and later recreating suspended parts. `hide` is `off` by default.

The `visible`, `shadow`, `trace`, `caustic`, and `globillum` modes are inherited down the scene DAG. Flags in instances lower (closer to the objects) override flags in instances higher up. The flags from the instance closest to the object are merged with the corresponding object flags. The resulting values become the effective flags for rendering. If no flags are specified in the relevant instances, only the object flags are used. For the exact definition of these flags refer to the Object section. The caustics mode bitmap contains five bits, and the desired behavior is the sum of 1 (to enable caustic casting), 2 (to enable caustic receiving), 4 (to disable caustic casting), and 8 (to disable caustic receiving). Obviously, 1 and 4, and 2 and 8, cannot be mixed, respectively. If mode is omitted, the default is 3 (enable casting and receiving). The fifth bit2.1contains an 'invisible to photons' flag, that is, if the fifth bit is set photons do not intersect this object. The globillum2.1mode bitmap is similar.

The `transform` statement is followed by 16 numbers that define a 4 `x` 4 matrix in row-major order. The matrix establishes the transformation from the parent coordinate space to the object space of the instanced element. If the instance is directly attached to the root instance group (see below), the parent coordinate space is world space. For example, the following matrix translates the instanced element to the coordinate (x, y, z):

        transform    1    0    0    0
            0    1    0    0
            0    0    1    0
            x    y    z    1

Instance transformations are ignored if the options element explicitly sets the coordinate space to camera space, using the `camera space` statement. This is not recommended. The parent-to-local space transformation direction has the effect that in order to move an instanced object one (local) unit in the (local) +X direction, xmust be decremented by 1.

The `motion transform` matrix specifies a transformation from parent space to local space for motion blurred geometry. If not specified, the instance transformation is used for the motion blur transformation. In this case the parent instance determines whether motion blur is active or not. Motion blur is activated by specifying a motion transformation in the scene DAG. This transformation is propagated through the scene DAG in the same way as the instance transformations. The `motion off` statement turns off all motion information inherited up to this point, as if the camera and all instances above did not have motion transforms. This can be used to disable motion transformations for a scene subtree.

If a motion transformation is specified in an object instance, the triangle vertex points of the tessellated geometry are transformed by the matrix product of the accumulated instance matrix and the inverse accumulated motion transformation matrix. The difference vector between the transformed and the untransformed triangle vertex point is used as a motion vector in local object space. If an object has motion vectors attached to the vertices, the motion vector calculated as described above is combined with the object motion vector. A motion transformation can be given for both object and camera instances. If a motion transformation is specified in a camera instance, the effective motion transformation for the triangle vertices is the matrix product of the relative instance and relative camera motion transformation.

The material_name is the name of a previously defined material. It is stored along with the instance. Instance materials are inherited down the scene DAG. Materials in instances lower in the scene DAG (closer to the leaves) override materials in instances higher up. The material defined lowest becomes the default material for any polygon or surface in a geometrical object that has no material of its own.

If a bracketed, comma-separated list of material_names is given, mental ray will use the n-th material in the list if the polygon or surface label is n. If the label exceeds the length of the list, the first material in the list is used. Polygon and surface labels can be specified in the object definition that have the `tagged` flag set. If this flag is not set, the first material in the list is used. The list may not be empty.

An instance may define parameters. Instance parameters are evaluated during scene preprocessing during preprocessing. Whenever the initial scene traversal finds an instance, it calls the inheritance shader defined in the options element with the parent instance parameters and the parameters of the new instance. The inheritance shader must then compute a new parameter set, which becomes the parent parameters for any future instances found in the element subtree below the new instance, if element is an instance group (if not, no sub-instances can exist and recursion ends). The inheritance shader is also called if there is no parent instance yet or if the new instance contains no parameters. The final parameter set created by the inheritance shader called for the bottom-level instance (which instances a camera, light, or object) is made available to shaders, in addition to the regular shader parameters.

The instance parameters must be declared just like shader parameters. The `declare` command must name the inheritance function, as specified in the `options` element. All instances share the same declaration. Note that this limits the portability of the scene -- it is difficult to merge it with another scene that uses a different parameter inheritance shader.

If `transform`, `motion transform`, and `material` are given without arguments, the respective feature is turned off. This is useful for incremental changes. It is not relevant for the initial definition because these features are off by default when an instance is created.

The element may be named in more than one instance. This is called `` multiple instancing.'' If two instances name the same object, the object appears twice in the scene, even though it is stored only once in the scene database. This greatly reduces memory consumption. For example, it is sufficient to create one wheel object for a car, and then instance it four times. All four instances will contain a different transformation matrices to place the wheels in four different locations. (This implies that multiple instancing is not useful in camera space mode because in this mode the transformations are ignored.) It is also possible to apply multiple instancing to object groups to replicate entire sub-scenes.

If the instanced item is a `` geometry shader'', the function is called with shader parameters and the scene element created by the shader is defined in the local coordinate space of the instance. The geometry shader is called just before tessellation takes place. The following example uses a geometry shader mib_geo_sphere:

        instance "sphere"
            geometry "mib_geo_sphere" ()
        end instance

This example creates a spherical object procedurally. It uses the syntax for anonymous shaders; as usual the named shader syntax using the `shader` keyword and named shader assignments using the ```=`'' sign can also be used. As usual, shader lists may be used; if the shader is correctly written all created objects are put in a group and instanced together. Named shaders created inside or outside procedural object definitions are in global scope and can be shared with other objects.

For a complete example for building scene graphs with instances and instance groups, see below.

## 2.7.10 Instance Groups

        instgroup "name"
            "name"
            ...
        end instgroup

Every scene consists of more than one element. There must be at least one camera and at least one object. In the simplest case, all cameras, lights, and objects can be collected into a single group, forming a ``flat scene'' because there is no hierarchy. Cameras, lights, and objects are never put into an instance group directly. Instead, an instance must be defined, one for each element, and the instance is then put into the group. (This is why it is called an ``instance group.'')

Instance groups can be nested. An instance group is placed into a parent instance group exactly like a camera, light, or object: an instance must be defined for the child instance group, and the instance is put into the parent instance group. As with other entities, it is possible to create more than one instance for an instance group; this allows multiple instancing of sub-scenes. There is no limit on the nesting depth of instance groups.

Since the only purpose of instance groups is as a container for instances, the syntax is very simple. After the name of the instance group, one or more names of instances follow. An incremental change to an instance group clears the old instance list (without deleting the instances themselves); to add or remove an instance in an instance group, the incremental change must respecify the entire instance list.

The top-level instance group has no instance. It is called the root instance group. The root instance group stands for the entire scene. It is passed to the `render` command to process the scene. More than one root instance group can exist, but only one can be processed at a time. Camera instances must always be attached to the root instance group, not a lower-level instance group, and it may not be multiply instanced to ensure unambiguity. Multiple cameras can exist in the root instance group, but only one can be passed to the `render` command.

#### Footnotes

... twenty-one.2.5
  The algorithms used impose no inherent limit. The limit may be increased in future versions.

Next: 2.8 Contours Up: 2. Scene Description Language Previous: 2.6 Commands