Triangle meshes are the most widely used representation of 3D geometry. Modern GPUs have dedicated hardware optimized for to support triangle rasterization and ray tracing.
Advantages of Triangles
Some of the advantages of triangles including that
- you will always have a valid triangle given any three points as long as they are not in a line
- We can interpolate on a triangle easily with the barycentric coordinates
- Triangles are always convex and coplanar, which simplifies many algorithms
What Makes a “good” Triangle Mesh
Triangle Shapes
See also: degenerate triangle
The shape of triangles are important. Long and thin triangles, often called “slivers,” can cause numerical instability in various computational applications.
A more sophisticated condition is called Delaunay (empty circumcircles). A mesh is Delaunay if no other vertices are in the circumcircle of of any triangles.
Degree of Mesh
Having regular vertex degree also makes a mesh “good.”
- For triangle meshes, a degree of 6 is considered optimal for interior vertices
- For quad meshes, a degree of 4 is ideal