Computational geometry: an introduction
Computational geometry: an introduction
Surface algorithms using bounds on derivatives
Computer Aided Geometric Design
Estimating subdivision depths for rational curves and surfaces
ACM Transactions on Graphics (TOG)
Guaranteed-quality mesh generation for curved surfaces
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Tessellation of trimmed NURB surfaces
Computer Aided Geometric Design
Improved surface bounds based on derivatives
Computer Aided Geometric Design
Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis
Computer Aided Geometric Design
Directional adaptive surface triangulation
Computer Aided Geometric Design
Piecewise Linear Approximation of Trimmed Surfaces
Geometric Modelling, Dagstuhl, Germany, 1993
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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.