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Conforming Delaunay Tetrahedronized Networks, Surface Reconstruction, Data Dependent Triangulations
"... The Triangulated Irregular Network (TIN) created by the 3DAnalyst extensions of ArcGIS 8.x and ArcView 3.x are based on the Delaunay empty circum circle criterion, which is believed to optimize how faces model a surface. This is not the case as this algorithm ignores the Zvalue of the surface poin ..."
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points. To get a better representation of the surface this papers describes a method based on the Delaunay Tetrahedronized Irregular Network (TEN). This TEN stores the measurements (linesoffsight to the surfacepoints). An ArcView algorithm is applied on this TEN to retrieve the TIN that represents
Piecewise Linear Complex represenation through Conforming Delaunay Tetrahedronization
"... The boundary of threedimensional objects is usually represented by Piecewise Linear Complexes (PLCs). A PLC is a set of vertices, segments and facets. The definition of PLCs requires that they must be closed under taking intersections; two segments can intersect only at a shared point, and two face ..."
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Delaunay Tetrahedronization (CDT) from these PLCs by adding Steiner points where necessary to obey the Delaunay empty circum sphere criterion. Once the CDT is generated, the PLC is part of this CDT. If a boundary marker is assigned to each facet of the PLC, all boundary faces on that facet in the final
Perturbations for Delaunay and weighted Delaunay 3D Triangulations
, 2011
"... The Delaunay triangulation and the weighted Delaunay triangulation are not uniquely defined when the input set is degenerate. We present a new symbolic perturbation that allows to always define these triangulations in a unique way, as soon as the points are not all coplanar. No flat tetrahedron exis ..."
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Cited by 1 (1 self)
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The Delaunay triangulation and the weighted Delaunay triangulation are not uniquely defined when the input set is degenerate. We present a new symbolic perturbation that allows to always define these triangulations in a unique way, as soon as the points are not all coplanar. No flat tetrahedron
Quality Meshing with Weighted Delaunay Refinement
 SIAM J. Comput
, 2002
"... Delaunay meshes with bounded circumradius to shortest edge length ratio have been proposed in the past for quality meshing. The only poor quality tetrahedra called slivers that can occur in such a mesh can be eliminated by the sliver exudation method. This method has been shown to work for periodic ..."
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Cited by 40 (7 self)
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quality tetrahedron including slivers. This success is achieved by combining the weight pumping method for sliver exudation and the Delaunay refinement method for boundary conformation. We show that an incremental weight pumping can be mixed seamlessly with vertex insertions in our weighted Delaunay
Functional Delaunay Refinement
 In 7th International Conference on Numerical Grid Generation in Computational Field Simulations
, 2000
"... : Given a complex of vertices, constraining segments (and planar straightline constraining facets in 3D) and an ffLipschitz control spacing function f() over the domain, an algorithm presented herein can generate a conforming mesh of Delaunay triangles (tetrahedra in 3D) whose circumradiustoshor ..."
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Cited by 2 (2 self)
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toshortest edge ratios are no greater than p 2 (2 in 3D). The triangle (tetrahedron) size is within a constant factor of f (). An implementation in 2D demonstrates that the algorithm generates excellent mesh. Keywords: unstructured mesh generation, delaunay refinement, control spacing, mesh conformity. 1
Sliverfree Three Dimensional Delaunay Mesh Generation
 PH.D THESIS, UIUC
, 2000
"... A key step in the nite element method is to generate wellshaped meshes in 3D. A mesh is wellshaped if every tetrahedron element has a small aspect ratio. It is an old outstanding problem to generate wellshaped Delaunay meshes in three or more dimensions. Existing algorithms do not completely solv ..."
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Cited by 12 (5 self)
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A key step in the nite element method is to generate wellshaped meshes in 3D. A mesh is wellshaped if every tetrahedron element has a small aspect ratio. It is an old outstanding problem to generate wellshaped Delaunay meshes in three or more dimensions. Existing algorithms do not completely
DELAUNAY TETRAHEDRALIZATIONS: HONOR DEGENERATED CASES
"... The definition of a Delaunay tetrahedralization (DT) of a set S of points is well known: a DT is a tetrahedralization of S in which every simplex (tetrahedron, triangle, or edge) is Delaunay. A simplex is Delaunay if all of its vertices can be connected by a circumsphere that encloses no other verte ..."
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The definition of a Delaunay tetrahedralization (DT) of a set S of points is well known: a DT is a tetrahedralization of S in which every simplex (tetrahedron, triangle, or edge) is Delaunay. A simplex is Delaunay if all of its vertices can be connected by a circumsphere that encloses no other
Perturbing Slivers in 3D Delaunay Meshes
 18TH INTERNATIONAL MESHING ROUNDTABLE (2009) 157173
, 2009
"... Isotropic tetrahedron meshes generated by Delaunay triangulations are known to contain a majority of wellshaped tetrahedra, as well as spurious sliver tetrahedra. As the slivers hamper stability of numerical simulations we aim at removing them while keeping the triangulation Delaunay for simplicit ..."
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Cited by 10 (1 self)
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Isotropic tetrahedron meshes generated by Delaunay triangulations are known to contain a majority of wellshaped tetrahedra, as well as spurious sliver tetrahedra. As the slivers hamper stability of numerical simulations we aim at removing them while keeping the triangulation Delaunay
Scanline forced Delaunay TENs for surface representation
"... The general idea that a Delaunay TIN (DT) is more appropriate than nonDelaunay TINs, due to ‘better ’ shaped triangles, might be true for many applications, but not for height dependent analytical queries. This is because the distribution of the triangle tessellation is defined in the twodimension ..."
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‘real ’ 3D triangulation construction method, resulting in a Tetrahedronized Irregular Network. This TEN is capable to store all kinds of surfacefeatures (as the targetpoints) and the scanlines as well. The scanlines are forced to split by adding Steiner points until they are part of the Delaunay TEN
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