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Title: A Walking Method for Non-Decomposition Intersection and Union of Arbitrary Polygons and Polyhedrons

Abstract

We present a method for computing the intersection and union of non- convex polyhedrons without decomposition in O(n log n) time, where n is the total number of faces of both polyhedrons. We include an accompanying Python package which addresses many of the practical issues associated with implementation and serves as a proof of concept. The key to the method is that by considering the edges of the original ob- jects and the intersections between faces as walking routes, we can e ciently nd the boundary of the intersection of arbitrary objects using directional walks, thus handling the concave case in a natural manner. The method also easily extends to plane slicing and non-convex polyhedron unions, and both the polyhedron and its constituent faces may be non-convex.

Authors:
 [1];  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1389941
Report Number(s):
LLNL-TR-737748
DOE Contract Number:  
AC52-07NA27344
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; non-convex; non-decomposition; intersection; union; directional walk

Citation Formats

Graham, M., and Yao, J. A Walking Method for Non-Decomposition Intersection and Union of Arbitrary Polygons and Polyhedrons. United States: N. p., 2017. Web. doi:10.2172/1389941.
Graham, M., & Yao, J. A Walking Method for Non-Decomposition Intersection and Union of Arbitrary Polygons and Polyhedrons. United States. doi:10.2172/1389941.
Graham, M., and Yao, J. Mon . "A Walking Method for Non-Decomposition Intersection and Union of Arbitrary Polygons and Polyhedrons". United States. doi:10.2172/1389941. https://www.osti.gov/servlets/purl/1389941.
@article{osti_1389941,
title = {A Walking Method for Non-Decomposition Intersection and Union of Arbitrary Polygons and Polyhedrons},
author = {Graham, M. and Yao, J.},
abstractNote = {We present a method for computing the intersection and union of non- convex polyhedrons without decomposition in O(n log n) time, where n is the total number of faces of both polyhedrons. We include an accompanying Python package which addresses many of the practical issues associated with implementation and serves as a proof of concept. The key to the method is that by considering the edges of the original ob- jects and the intersections between faces as walking routes, we can e ciently nd the boundary of the intersection of arbitrary objects using directional walks, thus handling the concave case in a natural manner. The method also easily extends to plane slicing and non-convex polyhedron unions, and both the polyhedron and its constituent faces may be non-convex.},
doi = {10.2172/1389941},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2017},
month = {8}
}

Technical Report:

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