Quality triangulations made smaller
نویسنده
چکیده
We study alternative types of Steiner points (to circumcenters) for computing quality guaranteed Delaunay triangulations in three dimensions. We show through experiments that their effective use results in smaller (in the number of tetrahedra) triangulations than the output of the traditional circumcenter refinement methods.
منابع مشابه
Triangulations with locally optimal Steiner points
We present two new Delaunay refinement algorithms, second an extension of the first. For a given input domain (a set of points or a planar straight line graph), and a threshold angle α, the Delaunay refinement algorithms compute triangulations that have all angles at least α. Our algorithms have the same theoretical guarantees as the previous Delaunay refinement algorithms. The original Delauna...
متن کاملConstruction of Three-Dimensional Improved-Quality Triangulations Using Local Transformations
Three-dimensional Delaunay triangulations are the most common form of three-dimensional triangulations known, but they are not very suitable for tetrahedral nite element meshes because they tend to contain poorly-shaped sliver tetrahedra. In this paper, we present an algorithm for constructing improved-quality triangulations with respect to a tetrahedron shape measure. This algorithm uses combi...
متن کاملDiscrete Laplace-Beltrami Operator on Sphere and Optimal Spherical Triangulations
In this paper we first modify a widely used discrete Laplace Beltrami operator proposed by Meyer et al over triangular surfaces, and then establish some convergence results for the modified discrete Laplace Beltrami operator over the triangulated spheres. A sequence of spherical triangulations which is optimal in certain sense and leads to smaller truncation error of the discrete Laplace Beltra...
متن کاملBalanced triangulations
Motivated by applications in numerical analysis, we investigate balanced triangulations, i.e. triangulations where all angles are strictly larger than π/6 and strictly smaller than π/2, giving the optimal lower bound for the number of triangles in the case of the square. We also investigate platonic surfaces, where we find for each one its respective optimal bound. In particular, we settle (aff...
متن کاملTopological Effects on Minimum Weight Steiner Triangulations
We are concerned with a long-standing classical problem in computational geometry: that of finding a minimum weight triangulation of a point set. A minimum weight triangulation is a triangulation which minimizes the sum of the Euclidean lengths of the edges used. Triangulations are very useful objects in the realm of applied computational geometry. By allowing for decompositions of space into s...
متن کامل