Optimal algorithms for approximate clustering
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
A quadratic time algorithm for the minmax length triangulation
SIAM Journal on Computing
Guaranteed-quality mesh generation for curved surfaces
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Linear-size nonobtuse triangulation of polygons
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Handbook of discrete and computational geometry
Approximating Uniform Triangular Meshes for Spheres
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Triangulating a convex polygon with fewer number of non-standard bars
Theoretical Computer Science
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
An inequality on the edge lengths of triangular meshes
Computational Geometry: Theory and Applications
Triangulating a convex polygon with small number of non-standard bars
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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We consider the problem of triangulating a convex polygon using n Steiner points under the following optimality criteria: (1) minimizing the overall edge length ratio; (2) minimizing the maximum edge length; and (3) minimizing the maximum triangle perimeter. We establish a relation of these problems to a certain extreme packing problem. Based on this relationship, we develop a heuristic producing constant approximations for all the optimality criteria above (provided n is chosen sufficiently large). That is, the produced triangular mesh is uniform in these respects.The method is easy to implement and runs in O(n2log n) time and O(n) space. The observed runtime is much less. Moreover, for criterion (1) the method works--within the same complexity and approximation bounds--for arbitrary polygons with possible holes, and for criteria (2) and (3) it does so for a large subclass.