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58
Parityconstrained Triangulations with Steiner points
, 2012
"... Let P ⊂ R 2 be a set of n points, of which k lie in the interior of the convex hull CH(P) of P. Let us call a triangulation T of P even (odd) if and only if all its vertices have even (odd) degree, and pseudoeven (pseudoodd) if at least the k interior vertices have even (odd) degree. On the one ha ..."
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Let P ⊂ R 2 be a set of n points, of which k lie in the interior of the convex hull CH(P) of P. Let us call a triangulation T of P even (odd) if and only if all its vertices have even (odd) degree, and pseudoeven (pseudoodd) if at least the k interior vertices have even (odd) degree. On the one
Mesh Generation And Optimal Triangulation
, 1992
"... We survey the computational geometry relevant to finite element mesh generation. We especially focus on optimal triangulations of geometric domains in two and threedimensions. An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some cri ..."
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Cited by 214 (7 self)
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criterion that measures the size, shape, or number of triangles. We discuss algorithms both for the optimization of triangulations on a fixed set of vertices and for the placement of new vertices (Steiner points). We briefly survey the heuristic algorithms used in some practical mesh generators.
Triangulations with Locally Optimal Steiner Points
, 2007
"... 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 ..."
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Cited by 8 (0 self)
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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
Even Triangulations of Planar Set of Points with Steiner Points
"... Let P ⊂ R 2 be a set of n points of which k are interior points. Let uscallatriangulationT ofP even ifallits vertices have even degree, and pseudoeven if at least the k interior vertices have even degree. (Pseudo) Even triangulations have one nice property; their vertices can be 3colored, see [2, ..."
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, 3, 4]. Since one can easily check that for some sets of points, such triangulation do not exist, we show an algorithm that constructs a set S of at most ⌊(k +2)/3 ⌋ Steiner points (extra points) along with a pseudoeven triangulation T of P ∪S = V(T). 1
Approximating the Minimum Weight Steiner Triangulation
, 1992
"... We show that the length of the minimum weight Steiner triangulation (MWST) of a point set can be approximated within a constant factor by a triangulation algorithm based on quadtrees. In O(n log n) time we can compute a triangulation with O(n) new points, and no obtuse triangles, that approximate ..."
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Cited by 15 (0 self)
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We show that the length of the minimum weight Steiner triangulation (MWST) of a point set can be approximated within a constant factor by a triangulation algorithm based on quadtrees. In O(n log n) time we can compute a triangulation with O(n) new points, and no obtuse triangles
TOPOLOGICAL EFFECTS ON MINIMUM WEIGHT STEINER TRIANGULATIONS
"... Abstract. Let mwt(X) denote the sum of the Euclidean edge lengths of a minimum weight triangulation of a point set X ∈ R 2. We investigate a curious property of some npoint sets X, which allow for an (n + 1) st point P (called a Steiner point) to give mwt(X ∪ {P}) < mwt(X). We call the regions o ..."
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Abstract. Let mwt(X) denote the sum of the Euclidean edge lengths of a minimum weight triangulation of a point set X ∈ R 2. We investigate a curious property of some npoint sets X, which allow for an (n + 1) st point P (called a Steiner point) to give mwt(X ∪ {P}) < mwt(X). We call the regions
Approximate Minimum Weight Steiner Triangulation in Three Dimensions
 In Proceedings of the Tenth Annual ACMSIAM Symposium on Discrete Algorithms
, 1999
"... Difficulty of minimum weight triangulation of a point set in R 2 is well known. In this paper we study the minimum weight triangulation problem for polyhedra and general obstacle set in three dimensions. The weight of a triangulation in three dimensions is assumed to be the total surface area of a ..."
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Cited by 3 (0 self)
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triangulation allowing Steiner points. We consider another setting called general obstacle set, where the convex hull of a set of n triangles is triangulated conforming to the input triangles. In this case we show that our method produces a triangulation of size O(n 3 log n) in time O(n 3 log 3 n
Isomorphic Triangulations with Minimal Number of Steiner Points (Extended Abstract)
, 1994
"... We present two algorithms for constructing isomorphic (i.e. adjacency preserving) triangulations of two simple n vertex polygons P, Q with k, l reflex vertices, respectively. The first algorithm computes an isomorphism by introducing at most O((k + l)²) Steiner points and has running time O(n + (k + ..."
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We present two algorithms for constructing isomorphic (i.e. adjacency preserving) triangulations of two simple n vertex polygons P, Q with k, l reflex vertices, respectively. The first algorithm computes an isomorphism by introducing at most O((k + l)²) Steiner points and has running time O(n + (k
Parallel Construction of Quadtrees and Quality Triangulations
, 1999
"... We describe e#cient PRAM algorithms for constructing unbalanced quadtrees, balanced quadtrees, and quadtreebased finite element meshes. Our algorithms take time O(log n) for point set input and O(log n log k) time for planar straightline graphs, using O(n + k/ log n) processors, where n measure ..."
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Cited by 72 (8 self)
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polygon), along with some extra vertices, called Steiner points. Not all triangulations, however, serve equally well; numerical and discretization error depend on the quality of the triangulation, meaning the shapes and sizes of triangles. A typical quality guarantee gives a lower bound on the minimum
Safe Steiner Points for Delaunay Refinement
, 2008
"... Summary. In mesh refinement for scientific computing or graphics, the input is a description of an input geometry, and the problem is to produce a set of additional “Steiner ” points whose Delaunay triangulation respects the input geometry, and whose points are wellspaced. Ideally, we would like th ..."
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Cited by 1 (0 self)
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Summary. In mesh refinement for scientific computing or graphics, the input is a description of an input geometry, and the problem is to produce a set of additional “Steiner ” points whose Delaunay triangulation respects the input geometry, and whose points are wellspaced. Ideally, we would like
Results 1  10
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58