Triangulation of NURBS surfaces through adaptive refinement
Jarosław Sugier · Machine Graphics & Vision International Journal archive · 2002
This paper discusses adaptive approach to the problem of automatic triangulation of NURBS surfaces. The algorithm presented here generates triangulation through the so-called adaptive refinement - a process carried out entirely in a parametric space with a variable triangle size adjusted to the local curvature of the surface, so that the imposed approximation error is not exceeded. The mesh is generated as an adaptive one right from the start, and no further decimation is required. Sample triangulations generated by the algorithm as well as a discussion of its computational complexity are included. Running times of the computer implementation confirm that an average computational cost of the algorithm is ∼ O(N), with N denoting the total number of triangles in the final mesh.