Approximation (called tessellation in Maya; see Introduction to Tessellation and Approximation) is the process mental ray for Maya uses to convert NURBS surfaces (or displacement mapped polygon meshes) to triangles. Triangles determine how smooth an object looks at closer distances to you (the camera). When poorly tessellated objects are close to the camera, they appear faceted; when they are further away, they don’t.
When rendering with mental ray for Maya, a set of approximation settings must be specified for each piece of geometry.
By default mental ray for Maya derives approximation settings from Maya’s tessellation settings. This produces results close to the look of Maya software rendered scenes, and is useful for those familiar with the behavior of those settings.
Alternatively, you can specify approximation settings more precisely for mental ray for Maya by using an approximation node.
The tessellation of a subdivision surface is controlled by subdivision approximation only, regardless of whether the subdivision surface is displacement mapped.
If only Basic tesselation (see Primary vs. secondary tessellation passes) is used, mental ray for Maya bases tessellation on the Curvature Toleranceattribute setting of the NURBS surface.
If the Advanced tessellation attributes are used but none of the secondary tessellation controls are active for an object, Parametric approximation is derived from Maya's primary tessellation controls. Otherwise, mental ray for Maya’s LDA approximation method is applied with values calculated from Maya secondary tessellation controls.
Primary tessellation creates a base triangulation, which is further tessellated until the secondary set of conditions are met. mental ray for Maya’s Parametric approximation method is comparable to Maya’s primary tessellation; the length/distance/angle (LDA) method is comparable to Maya’s secondary tessellation.