L. P. Chew. Guaranteed-quality mesh generation for curved surfaces. In Proc. 9th Annu. ACM Sympos. Comput. Geom., pages 274--280, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....uniform meshes. Ruppert [14] then introduced the first Delaunay insertion scheme to guarantee highquality two dimensional graded meshes. Shewchuk [16] improved the angle bound of Ruppert s scheme shortly after and proved that such a modification made the algorithm equivalent to another by Chew [3]. All of these schemes insert points at the circumcenters of triangles; other authors have proposed variations on the circumcenter as the location of point insertion. Rivara [13] suggested inserting a point at the midpoint of the common edge of the two terminal triangles of a set of triangles ....

L. Paul Chew. Guaranteed-quality mesh generation for curved surfaces. In Proceedings of the Ninth Annual Symposium on Computational Geometry, pages 274--280. Association for Computing Machinery, May 1993.

.... MTri or MLSeg from NULL RemoveY: removes an MY pointer from a Mesh2D does not delete it from dynamic memory removes it from MVert adjacency lists sets neighbour s incidences to NULL The signature for InsertLSeg is very similar; i.e. ErrCode InsertLSeg(MLSeg t, MVert vbuf[3], MTri nbuf[3] int cbuf[3] Mesh2D oppMesh) Both of these member functions return the logical ag ErrCode with value SUCCEEDED for a successful insertion, FAILED otherwise. The basic idea is to allow for a variety of possible ways to specify the data for the MTri to be inserted in this ....

.... MLSeg from NULL RemoveY: removes an MY pointer from a Mesh2D does not delete it from dynamic memory removes it from MVert adjacency lists sets neighbour s incidences to NULL The signature for InsertLSeg is very similar; i.e. ErrCode InsertLSeg(MLSeg t, MVert vbuf[3] MTri nbuf[3], int cbuf[3] Mesh2D oppMesh) Both of these member functions return the logical ag ErrCode with value SUCCEEDED for a successful insertion, FAILED otherwise. The basic idea is to allow for a variety of possible ways to specify the data for the MTri to be inserted in this mesh. The MVert ....

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L P Chew. Guaranteed-quality mesh generation for curved surfaces. In 9th Annual Symposium on Comp Geometry, pages 274-280, San Diego, California, 1993. ACM.

....meshing algorithms that provide some guarantee on the geometric quality of the meshes they produce. During the past decade, several researchers have proven results guaranteeing high quality in some geometric measure for triangular and tetrahedral meshes. In two dimensions, Ruppert s [4] and Chew s [5] algorithms are similar enough that Shewchuk was able to analyze the two within a uni ed framework [6] Shewchuk also presented a generalization of Ruppert s algorithm to three dimensions. In both two and three dimensions, the ratio of the circumradius of a cell to its shortest edge length can be ....

Chew, L. P. (1993). Guaranteed-quality mesh generation for curved surfaces. In Proceedings of the Ninth Annual Symposium on Computational Geometry, pages 274280. Association for Computing Machinery.

.... of the first is to partition a parameter domain into sets of adjacent elements that have the same specified properties [14, 50, 23] The key idea of the second is to progressively adapt an explicit mesh by performing elementary operations on its elements until it matches some specified properties [12, 44, 8, 7, 21, 46, 9]. Meshes for graphics Computer graphists mainly focus on remeshing for efficient visualization or geometry processing [25, 49] In an early work, Turk [52] proposed a re tiling technique that resamples an input mesh by first applying a relaxation method to initially randomly place points, by then ....

CHEW, L. P. Guaranteed-quality mesh generation for curved surfaces. In Proc. 9th Annu. ACM Sympos. Comput. Geom. (1993), pp.274--280.

....of the some of the components of our system that are especially relevant to this paper: The Surface Mesher produces triangular meshes for each of a model s geometric surfaces. This component Figure 1. Workflow for the Pipe problem produces surface meshes with certain quality guarantees [5]. The Generalized Mesher ( 4, 3] generates high quality meshes consisting of extruded triangular prisms, tetrahedral elements, and generalized prisms. These highly anisotropic elements are required for simulating viscous fluid flows required in regions near no slip boundaries, i.e. boundary ....

L. P. Chew. Guaranteed-quality mesh generation for curved surfaces. In Proceedings of the Ninth Symposium on Computational Geometry, pages 274--280. ACM Press, 1993.

....2D all these measures are equivalent up to constant factors [14] so the maxmin angle property of the DT means that it is a reasonable meshing technique for virtually all element quality measures. When coupled with algorithms for point insertion it is a basis for many refinement meshing techniques [1, 7, 18]. Figure 1: An illegal edge has a triangle whose circumcircle contains the opposite vertex of a neighboring triangle (left) By reconnecting ( flipping ) the edge, the circumcircles become disjoint (right) 2.2 Cutting and Delaunay flips Our problem, cutting in meshes, is di#erent from the ....

....on line segments connecting existing nodes, which implies that the overall resolution of the mesh does not increase. Some interactive simulations of deformable objects refine meshes on demand to provide more accurate results in the region of interest [10, 17, 22] Delaunay refinement algorithms [7, 18] seem to fit our framework of using Delaunay Triangulations, however more research is needed before this can be used in practice. Refinement algorithms need input geometries without small angles. Moreover, in 3D we are operating on a discretization of a curved surface, so it is not clear where to ....

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L. P. Chew. Guaranteed quality mesh generation for curved surfaces. In Annual ACM Symposium on Computational Geometry, pages 274--280, 1993.

....of triangles. 18 Minimizing the number of triangles is not always the goal of meshing algorithms. It can also be important to be able to control the mesh density, so that one can have a dense mesh in interesting areas and a coarse mesh in uninteresting areas. This is the setting studied by Chew [51]. He describes a meshing algorithm that allows the user to define a function that determines whether a triangle of the mesh is fine enough. The angles of the triangles produced by his algorithm are between 30 and 120 . Another nice aspect of his work is that the algorithm not only deals with ....

L. P. Chew. Guaranteed-quality mesh generation for curved surfaces. In Proc. 9th Annu. ACM Sympos. Cornput. Geom., pages 274-280, 1993.

....the reconstruction problem is a piecewise linear curve connecting points that are adjacent along the original curve from which the samples were taken. It is not immediately obvious how to generalize this idea to three dimensions. We use a definition of the correct set of triangles, used by Chew [7] and by Edelsbrunner and Shah [13] which we shall call the set of surface Delaunay triangles. Consider the three dimensional Voronoi diagram of S, and its intersection with F . The Voronoi diagram forms a partition of F into regions; this decomposition is the restricted Voronoi diagram of S in F ....

Chew, L.P., Guaranteed-quality mesh generation for curved surfaces, Proceedings of the ACM Symposium on Computational Geometry, (1993), pp. 274-280.

....deduced from the Voronoi graph of the surface vertices and the object can be decomposed into Delaunay tetrahedra. Di erent approaches have been proposed to constrain surfaces. One approach re nes surfaces, by adding points until every boundary triangles are forced into the Delaunay triangulation [10,26]. Some reconstruction methods produce directly Delaunay conforming surfaces [2,6,11] In this paper, we use the fact that we are considering iso surfaces. Therefore, we propose a di erent approach. We build iso surfaces that are directly included in the Delaunay tetrahedrization of their ....

L.P. Chew. Guaranteed-quality mesh generation for curved surfaces. In Proc. 9th Ann. Sympos. on Comput. Geom., pages 274-280, 1993.

....denition of the local feature size, the latter intersects the medial axis of S, the same is true for the former, which proves the lemma. 2 3. 2 Voronoi diagram on a surface We rst dene in this section the Voronoi diagram of a set of points restricted to a surface, following previous work by Chew [9] and Edelsbrunner and Shah [10] Denition 8 (Chew) The Voronoi diagram of A restricted to S is the (curved) cell complex obtained by intersecting each face of V or(A) with S. We denote it by V or S (A) Similarly, we can dene the Voronoi diagram of A restricted to O, denoted V or O (A) as the ....

L. P. Chew. Guaranteed-quality mesh generation for curved surfaces. In Proc. 9th Annu. ACM Sympos. Comput. Geom., pages 274280, 1993.

....Delaunay triangulations. The rst one, built from P, denes the implicit function. The second one, initialised from P, is the triangulation the new points are inserted into. It also provides the Delaunay facets tested for bi polarity. More precisely, we adapt Chew s curved surface meshing algorithm [11] as follows. To each bipolar facet is associated an error, which is the value h(c) at the center of the circle circumscribing the facet. We sort all the bipolar facets by decreasing errors and put all the facets whose errors are larger than a user specied error bound j in a priority queue Q. We ....

L. P. Chew. Guaranteed-quality mesh generation for curved surfaces. In Proc. 9th Annu. ACM Sympos. Comput. Geom., pages 274280, 1993.

....representation developed by our project [8] Surface Mesher Once the geometry model is produced, it is passed to the surface mesher component which produces triangular meshes for each of the model s geometric surfaces. This component produces surface meshes with certain quality guarantees [7]. Generalized Mesher Meshes and grids employed for simulating viscous fluid flows require highly anisotropic elements in regions near no slip boundaries, i.e. boundary layers. For such problems, topological adaptivity using cell types that are locally appropriate for the region being discretized ....

L. P. Chew. Guaranteed-quality mesh generation for curved surfaces. In Proceedings of the Ninth Symposium on Computational Geometry, pages 274--280. ACM Press, 1993. This issue is being addressed[3]

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L. P. Chew. Guaranteed-quality mesh generation for curved surfaces. In Proc. 9th Annu. ACM Sympos. Comput. Geom., pages 274--280, 1993.

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L.P. Chew. Guaranteed quality mesh generation for curved surfaces. In Proceedings of the ACM Symposium on Computational Geometry, pages 274--280, 1993.

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L.P. Chew. Guaranteed quality mesh generation for curved surfaces. In Proceedings of the ACM Symposium on Computational Geometry, pages 274--280, 1993.

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L.P. Chew. Guaranteed-quality mesh generation for curved surfaces. In Proceedings of the Ninth Annual Symposium on Computational Geometry, pages 274--280. ACM, 1993.

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L. P. Chew. Guaranteed-Quality Mesh Generation for Curved Surfaces. Proc. 9th Annu. ACM Sympos. Comput. Geom., 1993, pp 274-280.

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L. P. Chew. Guaranteed-quality mesh generation for curved surfaces. In Proc. 9th Annu. ACM Sympos. Comput. Geom., pages 274-280, 1993.

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L. P. Chew. Guaranteed-Quality Mesh Generation for Curved Surfaces. Proc. 9th Annu. ACM Sympos. Comput. Geom., 1993, pp 274-280. 2

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P. L. Chew. Guaranteed-quality mesh generation for curved surfaces. In Proceedings of the 9th Annual Symposium on Computational Geometry (SCG '93), pages 274-280. ACM Press, San Diego, CA, 1993.

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Chew LP. Guaranteed-quality mesh generation for curved surfaces. In Proceedings of the 9th Annual ACM Symposium on Computational Geometry 1993; 274 --280.

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L. P. Chew. Guaranteed-quality mesh generation for curved surfaces. Proc. 9th Annu. ACM Sympos. Comput. Geom., (1993), 274--280.

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Chew, L.P., "Guaranteed-Quality Mesh Generation for Curved Surfaces," ACM Press, Proceedings of the 9th Annual Symposium on Computational Geometry, San Diego, CA, 1993.

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L. P. Chew. Guaranteed-quality mesh generation for curved surfaces. Proc. 9th Annu. ACM Sympos. Comput. Geom., (1993), 274--280.

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L. P. Chew. Guaranteed-quality mesh generation for curved surfaces. Proc. 9th Annu. ACM Sympos. Comput. Geom., (1993), 274--280.

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