Coping with inconsistencies: a new approach to produce quality triangulations of polygonal domains with holes
Coping with inconsistencies: a new approach to produce quality triangulations of polygonal domains with holes
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处理不一致问题：一种生成带孔多边形域的高质量三角剖分的新方法
DOI：
10.1145/142675.142719
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
D. Souvaine
中科院分区：
文献类型：
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作者：
Elefterios A. Melissaratos;D. Souvaine
虽然有限元方法[20]、[21]、[10]、[2]、[12]、[22]、[9]、[8]、[5]在网格生成方面已经做了很多工作，但对同时生成“高质量”和小尺寸的网格却知之甚少。三角形网格的一个基本要求是它是一致的：一个三角剖分是相容的当且仅当一个三角形没有顶点位于另一个三角形的边上(见图3)。1)。如果对所有三角形[11]、[19]、[13]至少满足下列条件之一，则三角形网格是“高质量”的。非小角度：每个三角形的每个角的大小都大于某个常数C。非钝化：任何三角形的所有角都是~~。同时满足非小角度条件和非钝化条件的三角剖分称为精细三角剖分。漂亮的三角形)。据我们所知，唯一能保证网格质量和大小的工作是M.Bern，D.Eppstein和J.
Although much work has been done on the area of mesh generation for the Finite Element Method[20],[21],[10],[2],[12],[22],[9],[8],[5], very little is known on producing meshes which are provably of “high quality” and of small size at the same time. A basic requirement of a triangular mesh is that it be consistent: a triangulation is consistent iff there is no vertex of a triangle which lies on the edge of another triangle(see fig. 1). A triangular mesh is of “high quality” if at least one of the following conditions is true for all triangles[11],[19],[13]. no-small-angle: Every angle of every triangle has size greater than some constant c. non-obtuse: All angles of any triangle are~~.In this paper, a triangulation(resp. triangle) which satisfies both the no-small-angle condition and the non-obtuse condition shall be called a nice triangulation(resp. nice triangle). The only work, according to our knowledge, which guarantees both quality and size of the mesh is the work of M. Bern, D. Eppstein and J.