Render > Set NURBS
Tessellation
Render > Set NURBS
Tessellation > 
This method is exceptionally powerful for scenes in which the distance between the camera and the object changes (animation), and lets you save memory (and time) and enhance performance by preventing overtessellation.
Tessellation Mode
Maya automatically sets the optimal tessellation settings based on an object’s distance from the renderable camera(s), or lets you set them.
To adjust tessellation settings, you need to switch to Manual Mode.
Tessellation is based on the coverage and distance of the surface from the camera and the Automatic Mode settings.
Objects that are either close to the camera or occupy a significant amount of screen space are automatically tessellated with more triangles. Objects that are further from the camera or are smaller have fewer triangles.
Maya takes into consideration that distance changes over time if the surface or camera is animated, and tessellation is computed for a the range of frames set in Use Frame Range. Tessellation is evaluated and optimized at each frame, and the worst-case tessellation scenario requirements are determined and applied.
In automatic mode, the tessellation can be computed for the current frame or the frame range from the render settings or time slider.
Some of these settings appear and work for the Basic settings of Manual Mode too.
Use Frame Range
Available only in Automatic (default) Mode.
The tessellation computed by Automatic Tessellation depends on the distance of the surface from the camera. When the surface or camera is animated, this relationship changes over time.
Generally, when the surface is closest to the camera you need the best tessellation (the most triangles). If you know which frame this is, use Current Frame. Otherwise, Maya computes this for you by running up the animation for a specified frame range, evaluates the tessellation at each frame, and sets the tessellation attributes to provide optimal tessellation.
A progress bar at the bottom left of Maya’s window indicates the runup progress. You can also interrupt the runup for the tessellation evaluation by pressing the Esc key. During the interruption, the tessellation values are set and are valid up until the frame at which it was interrupted.
Maya uses the frame range set in Render Settings window.
Curvature Tolerance
You can determine how smooth the nickeling of the tessellation needs to be. When you adjust this setting, Maya automatically sets the Chord Height Ratio (an Advanced setting that is hidden, but automatically set in both Automatic (default) Mode and Manual Basic Mode).
In more complex scenes with many small objects, set the smaller objects to Low Quality. (This table applies only for manual mode; automatic mode sets the chord height, depending on the distance from the camera.)
Before adjusting these settings, adjust Curvature Tolerance to get the results you want.
When you adjust this setting, Maya automatically multiplies the values by the Per surf # isoparms in 3D (an Advanced setting that is hidden, but automatically set in both Automatic (default) Mode and Manual Basic Mode).
The higher the values, the more polygons produced. The U Divisions Factor and V Divisions Factor attributes should contain approximately the same value.
Use this to increase the number of triangles only along the boundary of an object. This lets you smooth the edges or prevent cracks between shared curves of adjacent surfaces without tessellating across the entire object, which incurs a high rendering time.
The higher the ratio, the smoother the edges and the higher the polygon count.
If you get artifacts in highlights along curved parts of the surface close to an edge, don’t use this attribute.
Adds more triangles where required in areas of curvature along the edges of the surface. The edge is the boundary of the NURBS surface, where one of the U or V parameters takes on its most extreme value. (This does not address the silhouette edges based on how the object is viewed from the camera.)
While extra triangles are primarily added along the edge, some are also added to the interior of the surface as needed to prevent cracking at T-junctions within the surface.
The ratio is the length of the tessellated triangle and the curve of the boundary.
Manual Mode
Select one of the following options:
Basic settings appear when you select this option. For descriptions of these settings, see Automatic Mode settings.
When you adjust Basic settings, Maya automatically sets the Advanced settings (which are hidden for simplicity) as follows (see Advanced Tessellation settings for details):
Advanced settings appear when you select this option. For descriptions of these settings, see Advanced Tessellation settings.
Advanced Tessellation settings
Available only in Manual mode with the Advanced option selected. If you have set the Curvature Tolerance (in either Automatic (default) mode or Manual Basic mode) to the highest setting and the object is still not smooth enough, use these settings to have more control over tessellation.
Mode U, Mode V
These are Primary Tessellation attributes (see Primary vs. secondary tessellation passes). These settings tell Maya how to tessellate the surface. The U and V values represent the U and V parametric dimensions of the NURBS surface. You can set these values differently to produce tessellation for each direction of your surface.
This is the most common mode. Divides each span, no matter how large or small, into the same number of subdivisions. Very small spans are divided into the same number of subdivisions as very large spans. The default setting is 3. Per span settings help to prevent cracks between joined surfaces where the spans match, which is particularly important for character building with multiple surfaces.
Creates a bounding box around the NURBS surface, projects it into screen space, and calculates the number of pixels in the space. Maya uses this number to guess at the per surface # of isoparms. The maximum value is 40. With this mode, the more screen space the object uses, the higher the value.
This is not good for animation if the camera or the object is moving because the bounding box would change constantly. If the bounding box changes so does the tessellation and texture jitter as a result. (Problems with highlights may occur as well.)
Chord height is a physical measurement based on object space units; it’s perpendicular distance at the centre of a triangle edge to the curve that defines the surface. If the actual distance measured is greater that the Chord Height value, the triangle is subdivided. Once it is subdivided, it will be checked again against the same criteria and the process will continue until the criteria is met. Chord height is measured in Object Space. The default is 0.1.
Chord Height is based on a default unit and doesn’t always work well for very small models as the chord height values on a small model will be smaller still.
When chord heights are calculated, if any are larger than 0.1, Maya subdivides the triangles and recomputes. This subdivision process continues until all triangles meet this criteria. The smaller the chord height, the better the approximation of the triangle to the surface curve. (This may be useful for industrial designers concerned with the accuracy of a model in relation to a prototype model.)
Specifies the maximum distance the center of a tessellated span can be from the actual NURBS surface.
Turn on to enable the Chord Height Ratio slider value.
Specifies the maximum ratio between the length of a span and the distance the center of that span is from the actual NURBS surface.
Takes the ratio between the chord height (d) and the Distance (D) between the two points where the triangle intersects the surface, and subtracts it from 1, as shown in the equation:
A Chord Height Ratio value of 0.997 and above produces very smooth tessellated surfaces. The default is 0.9830, which means d is very small compared to D (for example, 0.9830 = 1 - d/D). The closer to 1, the tighter the fit of the triangle to the surface. (This is best used in animations.)
Turn on to enable the Min Screen box.
Bases tessellation on a minimum screen size (default, 14 pixels). All triangles created during tessellation must fit within this screen size. If they don’t, the are further subdivided until they do. This option is good for still images with a setting off 11.0. This option is not recommended for animations because the tessellation will constantly change when an object is moving, causing textures to jitter or jump because the shading for a particular pixel will have different tessellations to deal with on each frame.
Tessellates a surface based on how far it is from the camera and uses the screen space to determine how much tessellation is required (instead of object or world space).
All triangles must fit within the specified area. The default is 14 pixels, which means all triangles must fit within a 14X14 pixel area on the screen. Triangles that do not meet this criteria are subdivided iteratively until they fall within the specified area. The smaller you set this value, the smaller the triangles must be to satisfy the criteria. Lowering this value can dramatically increase memory, so use caution.