Tessellation - Tessellations and Computer Models

Tessellations and Computer Models

In the subject of computer graphics, tessellation techniques are often used to manage datasets of polygons and divide them into suitable structures for rendering. Normally, at least for real-time rendering, the data is tessellated into triangles, which is sometimes referred to as triangulation. Tessellation is a staple feature of DirectX 11 and OpenGL.

In computer-aided design the constructed design is represented by a boundary representation topological model, where analytical 3D surfaces and curves, limited to faces and edges constitute a continuous boundary of a 3D body. Arbitrary 3D bodies are often too complicated to analyze directly. So they are approximated (tessellated) with a mesh of small, easy-to-analyze pieces of 3D volume—usually either irregular tetrahedra, or irregular hexahedra. The mesh is used for finite element analysis.

The mesh of a surface is usually generated per individual faces and edges (approximated to polylines) so that original limit vertices are included into mesh. To ensure that approximation of the original surface suits the needs of the further processing, three basic parameters are usually defined for the surface mesh generator:

• The maximum allowed distance between the planar approximation polygon and the surface (aka "sag"). This parameter ensures that mesh is similar enough to the original analytical surface (or the polyline is similar to the original curve).
• The maximum allowed size of the approximation polygon (for triangulations it can be maximum allowed length of triangle sides). This parameter ensures enough detail for further analysis.
• The maximum allowed angle between two adjacent approximation polygons (on the same face). This parameter ensures that even very small humps or hollows that can have significant effect to analysis will not disappear in mesh.

Algorithm generating mesh is driven by the parameters. Some computer analyses require adaptive mesh, which is made finer (using stronger parameters) in regions where the analysis needs more detail.

Some geodesic domes are designed by tessellating the sphere with triangles that are as close to equilateral triangles as possible.