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Image Warping with Scattered Data Interpolation Methods
, 1992
"... Image warping has many applications in art as well as in image processing. Usually, displacements are computed with mathematical functions or by transformations of a triangulation of control points. Here, different approaches based on scattered data interpolation methods are presented. These methods ..."
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Cited by 76 (3 self)
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Image warping has many applications in art as well as in image processing. Usually, displacements are computed with mathematical functions or by transformations of a triangulation of control points. Here, different approaches based on scattered data interpolation methods are presented. These methods provide smooth deformations with easily controllable behavior. The usefulness and performance of some selected classes of scattered data interpolation methods in this context is analyzed.
Aspects of Unstructured Grids and FiniteVolume Solvers for the Euler and NavierStokes Equations, von Karman Institute for Fluid Dynamics
 Lecture Series 199405, RhodeSaintGenèse
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Improved Incremental Randomized Delaunay Triangulation
, 1997
"... We propose a new data structure to compute the Delaunay triangulation of a set of points in the plane. It combines good worst case complexity, fast behavior on real data, and small memory occupation. The location ..."
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Cited by 43 (9 self)
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We propose a new data structure to compute the Delaunay triangulation of a set of points in the plane. It combines good worst case complexity, fast behavior on real data, and small memory occupation. The location
Shapes And Implementations In ThreeDimensional Geometry
, 1993
"... Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is often useful or required to compute what one might call the "shape" of the set. For that purpose, this thesis deals with the formal notion of the family of alpha shapes of a finite point ..."
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Cited by 37 (5 self)
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Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is often useful or required to compute what one might call the "shape" of the set. For that purpose, this thesis deals with the formal notion of the family of alpha shapes of a finite point set in three dimensional space. Each shape is a welldefined polytope, derived from the Delaunay triangulation of the point set, with a real parameter controlling the desired level of detail. Algorithms and data structures are presented that construct and store the entire family of shapes, with a quadratic time and space complexity, in the worst case.
Flipping Edges on Triangulations
, 1996
"... In this paper we study the problem of flipping edges in triangulations of polygons and point sets. We prove that if a polygon Q n has k reflex vertices, then any triangulation of Q n can be transformed to another triangulation of Q n with at most O(n + k 2 ) flips. We produce examples of polygons ..."
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Cited by 35 (7 self)
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In this paper we study the problem of flipping edges in triangulations of polygons and point sets. We prove that if a polygon Q n has k reflex vertices, then any triangulation of Q n can be transformed to another triangulation of Q n with at most O(n + k 2 ) flips. We produce examples of polygons with two triangulations T and T such that to transform T to T requires O(n 2 ) flips. These results are then extended to triangulations of point sets. We also show that any triangulation of an n point set always has n  4 2 edges that can be flipped. 1. Introduction Let P n = {v 1 , ..., v n } be a collection of points on the plane. A triangulation of P n is a partitioning of the convex hull Conv(P n ) of P n into a set of triangles T = {t 1 , ..., t m } with disjoint interiors in such a way that the vertices of each triangle t of T are points of P n . The elements of P n will be called the vertices of T and the edges of the triangles t 1 , ..., t m of T will be called the edges...
An Upper Bound for Conforming Delaunay Triangulations
 Discrete Comput. Geom
, 1993
"... A plane geometric graph C in ! 2 conforms to another such graph G if each edge of G is the union of some edges of C. It is proved that for every G with n vertices and m edges, there is a completion of a Delaunay triangulation of O(m 2 n) points that conforms to G. The algorithm that construct ..."
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Cited by 31 (6 self)
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A plane geometric graph C in ! 2 conforms to another such graph G if each edge of G is the union of some edges of C. It is proved that for every G with n vertices and m edges, there is a completion of a Delaunay triangulation of O(m 2 n) points that conforms to G. The algorithm that constructs the points is also described. Keywords. Discrete and computational geometry, plane geometric graphs, Delaunay triangulations, point placement. Appear in: Discrete & Computational Geometry, 10 (2), 197213 (1993) 1 Research of the first author is supported by the National Science Foundation under grant CCR8921421 and under the Alan T. Waterman award, grant CCR9118874. Any opinions, finding and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the National Science Foundation. Work of the second author was conducted while he was on study leave at the University of Illinois. 2 Department of Computer Scienc...
Edge Insertion for Optimal Triangulations
, 1993
"... The edgeinsertion paradigm improves a triangulation of a finite point set in R² iteratively by adding a new edge, deleting intersecting old edges, and retriangulating the resulting two polygonal regions. After presenting an abstract view of the paradigm, this paper shows that it can be used to o ..."
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Cited by 28 (3 self)
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The edgeinsertion paradigm improves a triangulation of a finite point set in R² iteratively by adding a new edge, deleting intersecting old edges, and retriangulating the resulting two polygonal regions. After presenting an abstract view of the paradigm, this paper shows that it can be used to obtain polynomial time algorithms for several types of optimal triangulations.
A PointPlacement Strategy for Conforming Delaunay Tetrahedralization
 Proceedings of the Eleventh Annual Symposium on Discrete Algorithms
, 2000
"... A strategy is presented to find a set of points which yields a Conforming Delaunay tetrahedralization of a threedimensional PiecewiseLinear Complex (PLC). This algorithm is novel because it imposes no angle restrictions on the input PLC. In the process, an algorithm is described that computes a ..."
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Cited by 20 (0 self)
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A strategy is presented to find a set of points which yields a Conforming Delaunay tetrahedralization of a threedimensional PiecewiseLinear Complex (PLC). This algorithm is novel because it imposes no angle restrictions on the input PLC. In the process, an algorithm is described that computes a planar conforming Delaunay triangulation of a Planar StraightLine Graph (PSLG) such that each triangle has a bounded circumradius, which may be of independent interest. 1 Introduction In many two and threedimensional geometric modeling problems, notably the numerical approximation of the solution to a Partial Differential Equation with a FiniteElement type method [SF73], it is very desirable to obtain a triangulation (tetrahedralization) that respects the domain of interest. The task of forming such decompositions, along with ensuring that the elements of the decompositions satisfy applicationspecific quality requirements, is sometimes referred to as unstructured mesh generation. Se...
The Edgeflipping Distance of Triangulations
, 1996
"... An edgeflipping operation in a triangulation T of a set of points in the plane is a local restructuring that changes T into a triangulation that differs from T in exactly one edge. The edgeflipping distance between two triangulations of the same set of points is the minimum number of edgeflippin ..."
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Cited by 19 (0 self)
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An edgeflipping operation in a triangulation T of a set of points in the plane is a local restructuring that changes T into a triangulation that differs from T in exactly one edge. The edgeflipping distance between two triangulations of the same set of points is the minimum number of edgeflipping operations needed to convert one into the other. In the context of computing the rotation distance of binary trees Sleator, Tarjan, and Thurston [7] show an upper bound of 2n \Gamma 10 on the maximum edgeflipping distance between triangulations of convex polygons with n nodes, n ? 12. Using volumetric arguments in hyperbolic 3space they prove that the bound is tight. In this paper we establish an upper bound on the edgeflipping distance between triangulations of a general set of points in the plane by showing that not more edgeflipping operations than the number of intersections between the edges of two triangulations are needed to transform these triangulations into another, and we pre...
Mesh Movement and Metamorphosis
 in Proceedings of the Tenth International Meshing Roundtable, Albuquerque, NM, 2001, Sandia National Laboratories
, 2001
"... Mesh coarsening and mesh enrichment are combined with an rre nement scheme to produce a exible approach for mesh adaptation of time evolving domains. The robustness of this method depends heavily on maintaining mesh quality during each adaptation cycle. This in turn is inuenced by the ability to i ..."
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Cited by 18 (0 self)
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Mesh coarsening and mesh enrichment are combined with an rre nement scheme to produce a exible approach for mesh adaptation of time evolving domains. The robustness of this method depends heavily on maintaining mesh quality during each adaptation cycle. This in turn is inuenced by the ability to identify and remove badly shaped elements after the rre nement stage. Measures of both element quality and element deformation can be de ned in terms of unitarily invariant matrix norms. The construction of these element deformation and quality measures is described, and details are provided of the three stages of the adaptation cycle.