Julien Basch, Leonidas J. Guibas, G. D. Ramkumar, Lyle Ramshaw  Home/Search
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Abstract: this paper is to define the notion of polyhedral tracings, which extends the classical notion of a polyhedron in exactly the same way a polygonal tracing extends the notion of a polygon. We also define the convolution B R of two polyhedral tracings B and R and show that it has the same desirable properties as in two dimensions. The technical challenge in getting this theory to work lies in how to extend normal polyhedra into tracings and, less obviously but equally importantly, how to orient... (Update)
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.... and Related Results The algorithm HeapSweep was developed in the context of a theory of polyhedral tracings and their convolution [6]. In a few words, one obtains the convolution of two polyhedra (a red and a blue) by first computing their geometric duals, projecting these...
...polygonal line of length k can be performed in O(log k) time. A theory of polyhedral tracings and their convolution is introduced in [1]. An interesting question there is whether the relationship between the convolution and the Minkowski sum explored in this paper can be...
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1.4: Polyhedral Tracings and their Convolution - Basch, Guibas, Ramkumar, Ramshaw (1996) (Correct)
0.2: Geometric Reasoning About Translational Motions - Schwarzer (2000) (Correct)
0.2: Sweeping Lines and Line Segments with a Heap - Basch, Guibas, Ramkumar (1997) (Correct)
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0.5: Kinetic Data Structures - Basch (1999) (Correct)
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BibTeX entry: (Update)
J. Basch, L.J. Guibas, G.D. Ramkumar, and L. Ramshaw. Polyhedral tracings and their convolution. In Proc. 2nd Workshop on Algorithmic Fundations of Robotics, 1996. http://citeseer.nj.nec.com/article/basch96polyhedral.html More
@misc{ basch96polyhedral,
author = "J. Basch and L. Guibas and G. Ramkumar and L. Ramshaw",
title = "Polyhedral tracings and their convolution",
text = "J. Basch, L.J. Guibas, G.D. Ramkumar, and L. Ramshaw. Polyhedral tracings
and their convolution. In Proc. 2nd Workshop on Algorithmic Fundations of
Robotics, 1996.",
year = "1996",
url = "citeseer.nj.nec.com/article/basch96polyhedral.html" }
Citations (may not include all citations):474 Kluwer Academic Publishers (context) - Latombe, Planning - 1991
216 Primitives for the manipulation of general subdivisions and .. (context) - Guibas, Stolfi - 1985
133 Algorithms for reporting and counting geometric intersection.. (context) - Bentley, Ottmann - 1979
128 Spatial planning: A configuration space approach (context) - Lozano-P'erez - 1983
73 A kinetic framework for computational geometry (context) - Guibas, Ramshaw et al. - 1983
49 Algorithms for bichromatic line segment problems and polyhed.. (context) - Chazelle, Edelsbrunner et al. - 1994
39 Computing convolutions by reciprocal search (context) - Guibas, Seidel - 1987
37 The complexity and construction of many faces in arrangement.. (context) - Edelsbrunner, Guibas et al. - 1990
36 Generation of configuration space obstacles: The case of mov.. (context) - Bajaj, Kim - 1989
31 Solid-interpolating deformations: construction and animation.. (context) - Kaul, Rossignac - 1992
21 Differential Manifolds (context) - Lang - 1972
19 Red-blue intersection detection algorithms (context) - Agarwal, Sharir - 1990
8 Agrels and bips: Metamorphosis as a b'ezier curve in the spa.. (context) - Rossignac, Kaul - 1994
5 Operations on constructible functions (context) - Schapira
4 Computing minkowski sums of regular polyhedra (context) - Kaul, O'Connor - 1993
4 Reporting red-blue intersections between connected sets of l.. (context) - Basch, Guibas et al.
3 Algorithms to compute the convolution and minkowski sum oute.. (context) - Ramkumar - 1996
1 Orienting the fiber product of smooth manifolds (context) - Basch, Ramshaw
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