The Experts below are selected from a list of 12 Experts worldwide ranked by ideXlab platform
Michael Ortiz - One of the best experts on this subject based on the ideXlab platform.
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Variational Delaunay approach to the generation of tetrahedral finite element meshes
International Journal for Numerical Methods in Engineering, 2001Co-Authors: Petr Krysl, Michael OrtizAbstract:We describe an algorithm which generates tetrahedral decomposition of a general solid body, whose surface is given as a collection of triangular Facets. The principal idea is to modify the constraints in such a way as to make them appear in an unconstrained triangulation of the vertex set apriori. The vertex set positions are randomized to guarantee existence of a unique triangulation which satisfies the Delaunay empty-sphere property. (Algorithms for robust, parallelized construction of such triangulations are available.) In order to make the boundary of the solid appear as a collection of tetrahedral faces, we iterate two operations, edge flip and edge split with the insertion of additional vertex, until all of the boundary Facets are present in the tetrahedral mesh. The outcome of the vertex insertion is another triangulation of the input surfaces, but one which is represented as a subset of the tetrahedral faces. To determine if a Constraining Facet is present in the unconstrained Delaunay triangulation of the current vertex set, we use the results of Rajan which re-formulate Delaunay triangulation as a linear programming problem.
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Variational delaunay approach to the generation of tetrahedral finite element meshes
1999Co-Authors: Petr Krysl, Michael OrtizAbstract:Abstract. We describe an algorithm which generates tetrahedral decomposition of a general solid body, whose surface is given as a collection of triangular Facets. The principle idea is to modify the constraints in such a way as to make them appear in an unconstrained triangulation of the vertex set à priori. The vertex set positions are randomized to guarantee existence of a unique triangulation which satisfies the Delaunay empty-sphere property. (Algorithms for robust, parallelized construction of such triangulations are available.) In order to make the boundary of the solid appear as a collection of tetrahedral faces, we iterate two operations, edge flip and edge split with the insertion of additional vertex, until all of the boundary Facets are present in the tetrahedral mesh. The outcome of the vertex insertion is another triangulation of the input surfaces, but one which is represented as a subset of the tetrahedral faces. To determine if a Constraining Facet is present in the unconstrained Delaunay triangulation of the current vertex set, we use the results of Rajan which re-formulate Delaunay triangulation as a linear programming problem
Petr Krysl - One of the best experts on this subject based on the ideXlab platform.
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Variational Delaunay approach to the generation of tetrahedral finite element meshes
International Journal for Numerical Methods in Engineering, 2001Co-Authors: Petr Krysl, Michael OrtizAbstract:We describe an algorithm which generates tetrahedral decomposition of a general solid body, whose surface is given as a collection of triangular Facets. The principal idea is to modify the constraints in such a way as to make them appear in an unconstrained triangulation of the vertex set apriori. The vertex set positions are randomized to guarantee existence of a unique triangulation which satisfies the Delaunay empty-sphere property. (Algorithms for robust, parallelized construction of such triangulations are available.) In order to make the boundary of the solid appear as a collection of tetrahedral faces, we iterate two operations, edge flip and edge split with the insertion of additional vertex, until all of the boundary Facets are present in the tetrahedral mesh. The outcome of the vertex insertion is another triangulation of the input surfaces, but one which is represented as a subset of the tetrahedral faces. To determine if a Constraining Facet is present in the unconstrained Delaunay triangulation of the current vertex set, we use the results of Rajan which re-formulate Delaunay triangulation as a linear programming problem.
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Variational delaunay approach to the generation of tetrahedral finite element meshes
1999Co-Authors: Petr Krysl, Michael OrtizAbstract:Abstract. We describe an algorithm which generates tetrahedral decomposition of a general solid body, whose surface is given as a collection of triangular Facets. The principle idea is to modify the constraints in such a way as to make them appear in an unconstrained triangulation of the vertex set à priori. The vertex set positions are randomized to guarantee existence of a unique triangulation which satisfies the Delaunay empty-sphere property. (Algorithms for robust, parallelized construction of such triangulations are available.) In order to make the boundary of the solid appear as a collection of tetrahedral faces, we iterate two operations, edge flip and edge split with the insertion of additional vertex, until all of the boundary Facets are present in the tetrahedral mesh. The outcome of the vertex insertion is another triangulation of the input surfaces, but one which is represented as a subset of the tetrahedral faces. To determine if a Constraining Facet is present in the unconstrained Delaunay triangulation of the current vertex set, we use the results of Rajan which re-formulate Delaunay triangulation as a linear programming problem
Jonathan Richard Shewchuk - One of the best experts on this subject based on the ideXlab platform.
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Symposium on Computational Geometry - A condition guaranteeing the existence of higher-dimensional constrained Delaunay triangulations
Proceedings of the fourteenth annual symposium on Computational geometry - SCG '98, 1998Co-Authors: Jonathan Richard ShewchukAbstract:Let X be a complex of vertices and piecewise linear Constraining Facets embedded in Ed. Say that a simplex is strongly Delaunay if its vertices are in X and there exists a sphere that passes through its vertices but passes through and encloses no other vertex. Then X has a d-dimensional constrained Delaunay triangulation if each k-dimensional Constraining Facet in X with k d 2 is a union of strongly Delaunay k-simplices. This theorem is especially useful in E3 for forming tetrahedralizations that respect specified planar Facets. If the bounding segments of these Facets are subdivided so that the subsegments are strongly Delaunay, then a constrained tetrahedralization exists. Hence, fewer vertices are needed than in the most common practice in the literature, wherein additional vertices are inserted in the relative interiors of Facets to form a conforming (but unconstrained) Delaunay tetrahedralization.
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A Condition Guaranteeing the Existence of Higher-Dimensional Constrained Delaunay Triangulations
1998Co-Authors: Jonathan Richard ShewchukAbstract:Let X be a complex of vertices and piecewise linear Constraining Facets embedded in E d . Say that a simplex is strongly Delaunay if its vertices are in X and there exists a sphere that passes through its vertices but passes through and encloses no other vertex. Then X has a d-dimensional constrained Delaunay triangulation if each k-dimensional Constraining Facet in X with k d \Gamma 2 is a union of strongly Delaunay k-simplices. This theorem is especially useful in E 3 for forming tetrahedralizations that respect specified planar Facets. If the bounding segments of these Facets are subdivided so that the subsegments are strongly Delaunay, then a constrained tetrahedralization exists. Hence, fewer vertices are needed than in the most common practice in the literature, wherein additional vertices are inserted in the relative interiors of Facets to form a conforming (but unconstrained) Delaunay tetrahedralization. 1 Introduction Many applications can benefit from triangulations..