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Hamiltonian triangulations for . . .
"... Highperformance rendering engines in computer graphics are often pipelined, and their speed is bounded by the rate at which triangulation data can be sent into the machine. To reduce the data rate, it is desirable to order the triangles so that consecutive triangles share a face, meaning that only ..."
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that the problem is NPcomplete for polygons with holes. Show how to add Steiner points to a given triangulation in order to create Hamiltonian triangulations which avoid narrow angles, thereby yielding guaranteedquality Hamiltonian mesh generation. Give an encoding sequence for any triangulation whose length
COMPATIBLE TRIANGULATIONS AND POINT PARTITIONS BY SERIESTRIANGULAR GRAPHS
"... Abstract. We introduce seriestriangular graph embeddings and show how to partition point sets with them. This result is then used to prove an upper bound on the number of Steiner points needed to obtain compatible triangulations of point sets. The problem is generalized to finding compatible triang ..."
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Abstract. We introduce seriestriangular graph embeddings and show how to partition point sets with them. This result is then used to prove an upper bound on the number of Steiner points needed to obtain compatible triangulations of point sets. The problem is generalized to finding compatible
Optimal Point Placement for Mesh Smoothing
, 1997
"... We study the problem of moving a vertex in a finite element mesh to optimize the shapes of adjacent triangles. We show that many such problems can be solved in linear time using generalized linear programming. We also give efficient algorithms for some mesh smoothing problems that do not fit into th ..."
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Cited by 89 (5 self)
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into the generalized linear programming paradigm. 1 Introduction Unstructured mesh generation, a key step in the finite element method, can be divided into two stages. In point placement, the input domain is augmented by Steiner points and a preliminary mesh is formed, typically by Delaunay triangulation. In mesh
Towards Compatible Triangulations
, 2001
"... We state the following conjecture: any two planar npoint sets (that agree on the number of convex hull points) can be triangulated in a compatible manner, i.e., such that the resulting two planar graphs are isomorphic. The conjecture is proved true for point sets with at most three interior points. ..."
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Cited by 4 (0 self)
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. We further exhibit a class of point sets which can be triangulated compatibly with any other set that satisfies the obvious size and hull restrictions. Finally, we prove that adding a small number of Steiner points (the number of interior points minus two) always allows for compatible triangulations.
Nonequivalent partitions of dtriangles with Steiner points
, 2004
"... In this paper we present lower and upper bounds for the number of equivalence classes of dtriangles with additional or Steiner points. We also study the number of possible partitions that may appear by bisecting a tetrahedron with Steiner points at the midpoints of its edges. This problem arises, f ..."
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, for example, when refining a 3D triangulation by bisecting the tetrahedra. To begin with, we look at the analogous 2D case, and then the 1irregular tetrahedra (tetrahedra with at most one Steiner point on each edge) are classified into equivalence classes, and each element of the class is subdivided
Approximating the Minimum Weight Triangulation
, 1991
"... 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 approximat ..."
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Cited by 9 (4 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
PolynomialSize Nonobtuse Triangulation Of Polygons
, 1992
"... We describe methods for triangulating polygonal regions of the plane so that no triangle has a large angle. Our main result is that a polygon with n sides can be triangulated with O(n 2 ) nonobtuse triangles. We also show that any triangulation (without Steiner points) of a simple polygon has a ..."
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Cited by 34 (8 self)
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We describe methods for triangulating polygonal regions of the plane so that no triangle has a large angle. Our main result is that a polygon with n sides can be triangulated with O(n 2 ) nonobtuse triangles. We also show that any triangulation (without Steiner points) of a simple polygon has
ENTROPY, TRIANGULATION, AND POINT LOCATION IN PLANAR SUBDIVISIONS
, 2009
"... A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More specifically, an algorithm is presented that preprocesses a connecte ..."
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Cited by 3 (2 self)
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bound on the expected number of pointline comparisons performed by any linear decision tree for point location in G under the query distribution D. The preprocessing algorithm runs in O(n log n) time and produces a data structure of size O(n). These results are obtained by creating a Steiner
Time complexity of practical parallel steiner point insertion algorithms
 In SPAA ’04: Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
, 2004
"... An effective method in practice to compute quality Delaunay triangulations is to apply parallel refinements that insert Steiner points whose prestars in the triangulation do not overlap. We show that these algorithms can be implemented in O(logm) time using m processors, where m is the output size. ..."
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Cited by 8 (2 self)
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An effective method in practice to compute quality Delaunay triangulations is to apply parallel refinements that insert Steiner points whose prestars in the triangulation do not overlap. We show that these algorithms can be implemented in O(logm) time using m processors, where m is the output size
Converting Triangulations to Grids
, 1998
"... This paper outlines a simple and fast method for conversion of unstructured triangulations to connected grids. The conversion strategy is as follows: we begin by using mesh decimation by edge shrinks to define a triangulated base complex and parametrize the original mesh points on the faces of the b ..."
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This paper outlines a simple and fast method for conversion of unstructured triangulations to connected grids. The conversion strategy is as follows: we begin by using mesh decimation by edge shrinks to define a triangulated base complex and parametrize the original mesh points on the faces
Results 11  20
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