Guaranteed-quality mesh generation for curved surfaces
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Anisotropic mesh transformations and optimal error control
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Lepp terminal centroid method for quality triangulation
Computer-Aided Design
Lepp terminal centroid method for quality triangulation: a study on a new algorithm
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
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The use of edge based refinement in general, and Delaunay terminal edge refinement in particular are well established for adaptive meshing, but largely on a heuristic basis. In this paper, we present some theoretical results on geometric improvement, and it limitations, for these methods. Angle bounds for simple longest edge bisection are reviewed and extended. Terminal edges are local maximal edges in a mesh; two additional bounds that apply to simple bisection of terminal edges in Delaunay meshes are presented. The angle properties of Delaunay insertion of the midpoint of a terminal edge are described.