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Robert L. Scot Drysdale

Other affiliations: PARC, Brown University, Carnegie Mellon University  ...read more
Bio: Robert L. Scot Drysdale is an academic researcher from Dartmouth College. The author has contributed to research in topics: Voronoi diagram & Minimum-weight triangulation. The author has an hindex of 17, co-authored 33 publications receiving 1636 citations. Previous affiliations of Robert L. Scot Drysdale include PARC & Brown University.

Papers
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Journal ArticleDOI
TL;DR: The algorithm presented is an improvement of a previous known result which takes $O(Nc^{\sqrt {\log N} } )$ time and is shown to be applicable under a more general metric if certain conditions are satisfied.
Abstract: In this paper we study the Voronoi diagram for a set of N line segments and circles in the Euclidean plane. The diagram is a generalization of the Voronoi diagram for a set of points in the plane a...

326 citations

Proceedings ArticleDOI
01 Sep 1995
TL;DR: An experimental comparison of a number of different algorithms for computing the Deluanay triangulation and analyzes the major high-level primitives that algorithms use and does an experimental analysis of how often implementations of these algorithms perform each operation.
Abstract: This paper presents an experimental comparison of a number of different algorithms for computing the Deluanay triangulation. The algorithms examined are: Dwyer’s divide and conquer algorithm, Fortune’s sweepline algorithm, several versions of the incremental algorithm (including one by Ohya, Iri, and Murota, a new bucketing-based algorithm described in this paper, and Devillers’s version of a Delaunay-tree based algorithm that appears in LEDA), an algorithm that incrementally adds a correct Delaunay triangle adjacent to a current triangle in a manner similar to gift wrapping algorithms for convex hulls, and Barber’s convex hull based algorithm. Most of the algorithms examined are designed for good performance on uniformly distributed sites. However, we also test implementations of these algorithms on a number of non-uniform distibutions. The experiments go beyond measuring total running time, which tends to be machine-dependent. We also analyze the major high-level primitives that algorithms use and do an experimental analysis of how often implementations of these algorithms perform each operation.

171 citations

Journal ArticleDOI
TL;DR: An experimental comparison of a number of different algorithms for computing the Delaunay triangulation is presented and an experimental analysis of how often implementations of these algorithms perform each operation is done.
Abstract: This paper presents an experimental comparison of a number of different algorithms for computing the Delaunay triangulation. The algorithms examined are: Dwyer's divide and conquer algorithm, Fortune's sweepline algorithm, several versions of the incremental algorithm (including one by Ohya, Iri and Murota, a new bucketing-based algorithm described in this paper, and Devillers's version of a Delaunay-tree based algorithm that appears in LEDA), an algorithm that incrementally adds a correct Delaunay triangle adjacent to a current triangle in a manner similar to gift wrapping algorithms for convex hulls, and Barber's convex hull based algorithm. Most of the algorithms examined are designed for good performance on uniformly distributed sites. However, we also test implementations of these algorithms on a number of non-uniform distributions. The experiments go beyond measuring total running time, which tends to be machine-dependent. We also analyze the major high-level primitives that algorithms use and do an experimental analysis of how often implementations of these algorithms perform each operation.

137 citations

Journal ArticleDOI
TL;DR: A divide-and-conquer approach similar to the ones used by Bentley is used and a new notion of Voronoi diagram is introduced along with a method for efficient computation of certain functions over paths of a tree.
Abstract: We consider the following problem: Given a rectangle containing N points, find the largest area subrectangle with sides parallel to those of the original rectangle which contains none of the given points. If the rectangle is a piece of fabric or sheet metal and the points are flaws, this problem is finding the largest-area rectangular piece which can be salvaged. A previously known result [13] takes $O(N^2 )$ worst-case and $O(N\log ^2 N)$ expected time. This paper presents an $O(N\log ^3 N)$ time, $O(N\log N)$ space algorithm to solve this problem. It uses a divide-and-conquer approach similar to the ones used by Bentley [1] and introduces a new notion of Voronoi diagram along with a method for efficient computation of certain functions over paths of a tree.

133 citations

Journal ArticleDOI
TL;DR: A technique designed to move the NC proof process into software is described, which outputs a color-coded graphics display of the machined surface that shows out-of-tolerance areas.
Abstract: The numerically controlled (NC) machining of sculptured surfaces is an error-prone process often requiring several attempts before an error-free NC program is produced. A technique designed to move the NC proof process into software is described. The system outputs a color-coded graphics display of the machined surface that shows out-of-tolerance areas. To gain efficiency, surface curvature and cutting-tool size are used as inputs to a surface discretization algorithm, which guarantees that a user-defined level of simulation accuracy is achieved. The simulation time grows linearly in both desired accuracy and in the number of tool movements. In typical test cases, NC programs for complex automotive body panels were simulated and verified in CPU times that ranged between 5 and 30 minutes. >

133 citations


Cited by
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MonographDOI
01 Jan 2006
TL;DR: This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms, into planning under differential constraints that arise when automating the motions of virtually any mechanical system.
Abstract: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

6,340 citations

Journal ArticleDOI
TL;DR: The Voronoi diagram as discussed by the authors divides the plane according to the nearest-neighbor points in the plane, and then divides the vertices of the plane into vertices, where vertices correspond to vertices in a plane.
Abstract: Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer graphics, computer-aided design, robotics, pattern recognition, and operations research—give rise to problems that inherently are geometrical. This is one reason computational geometry has attracted enormous research interest in the past decade and is a well-established area today. (For standard sources, we refer to the survey article by Lee and Preparata [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner [1987bl.) Readers familiar with the literature of computational geometry will have noticed, especially in the last few years, an increasing interest in a geometrical construct called the Voronoi diagram. This trend can also be observed in combinatorial geometry and in a considerable number of articles in natural science journals that address the Voronoi diagram under different names specific to the respective area. Given some number of points in the plane, their Voronoi diagram divides the plane according to the nearest-neighbor

4,236 citations

Book
01 Jan 1987
TL;DR: This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems with an important role in this study.
Abstract: This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems. Combinatorial investigations play an important role in this study.

2,284 citations

Book ChapterDOI
27 May 1996
TL;DR: Triangle as discussed by the authors is a robust implementation of two-dimensional constrained Delaunay triangulation and Ruppert's Delaunayer refinement algorithm for quality mesh generation, and it is shown that the problem of triangulating a planar straight line graph (PSLG) without introducing new small angles is impossible for some PSLGs.
Abstract: Triangle is a robust implementation of two-dimensional constrained Delaunay triangulation and Ruppert's Delaunay refinement algorithm for quality mesh generation. Several implementation issues are discussed, including the choice of triangulation algorithms and data structures, the effect of several variants of the Delaunay refinement algorithm on mesh quality, and the use of adaptive exact arithmetic to ensure robustness with minimal sacrifice of speed. The problem of triangulating a planar straight line graph (PSLG) without introducing new small angles is shown to be impossible for some PSLGs, contradicting the claim that a variant of the Delaunay refinement algorithm solves this problem.

2,268 citations

Journal ArticleDOI
Steven Fortune1
TL;DR: A geometric transformation is introduced that allows Voronoi diagrams to be computed using a sweepline technique and is used to obtain simple algorithms for computing the Vor onoi diagram of point sites, of line segment sites, and of weighted point sites.
Abstract: We introduce a geometric transformation that allows Voronoi diagrams to be computed using a sweepline technique. The transformation is used to obtain simple algorithms for computing the Voronoi diagram of point sites, of line segment sites, and of weighted point sites. All algorithms haveO(n logn) worst-case running time and useO(n) space.

1,209 citations