TY - JOUR
T1 - Trimming local and global self-intersections in offset curves/surfaces using distance maps
AU - Seong, Joon Kyung
AU - Elber, Gershon
AU - Kim, Myung Soo
N1 - Funding Information:
We would like to thank the anonymous reviewers for their invaluable comments. All the algorithms and figures presented in this paper were implemented and generated using the IRIT solid modeling system [11] developed at the Technion, Israel. This work was supported in part by European FP6 NoE grant 506766 (AIM@SHAPE), in part by the Israel Science Foundation (grant No. 857/04), in part by the Korean Ministry of Information and Communication (MIC) under the Program of IT Research Center on CGVR and in part by grant No. R01-2002-000-00512-0 from the Basic Research Program of the Korea Science and Engineering Foundation (KOSEF).
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2006/3
Y1 - 2006/3
N2 - A robust and efficient algorithm for trimming both local and global self-intersections in offset curves and surfaces is presented. Our scheme is based on the derivation of a rational distance map between the original curve or surface and its offset. By solving a bivariate polynomial equation for an offset curve or a system of three polynomial equations for an offset surface, all local and global self-intersection regions in offset curves or surfaces can be detected. The zero-set of polynomial equation(s) corresponds to the self-intersection regions. These regions are trimmed by projecting the zero-set into an appropriate parameter space. The projection operation simplifies the analysis of the zero-set, which makes the proposed algorithm numerically stable and efficient. Furthermore, in a post-processing step, a numerical marching method is employed, which provides a highly precise scheme for self-intersection elimination in both offset curves and surfaces. The effectiveness of our approach is demonstrated using several experimental results.
AB - A robust and efficient algorithm for trimming both local and global self-intersections in offset curves and surfaces is presented. Our scheme is based on the derivation of a rational distance map between the original curve or surface and its offset. By solving a bivariate polynomial equation for an offset curve or a system of three polynomial equations for an offset surface, all local and global self-intersection regions in offset curves or surfaces can be detected. The zero-set of polynomial equation(s) corresponds to the self-intersection regions. These regions are trimmed by projecting the zero-set into an appropriate parameter space. The projection operation simplifies the analysis of the zero-set, which makes the proposed algorithm numerically stable and efficient. Furthermore, in a post-processing step, a numerical marching method is employed, which provides a highly precise scheme for self-intersection elimination in both offset curves and surfaces. The effectiveness of our approach is demonstrated using several experimental results.
KW - Distance map
KW - Global self-intersection
KW - Local self-intersection
KW - Offset curve
KW - Offset surface
KW - Zero-set computation
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U2 - 10.1016/j.cad.2005.08.002
DO - 10.1016/j.cad.2005.08.002
M3 - Article
AN - SCOPUS:31344432184
VL - 38
SP - 183
EP - 193
JO - CAD Computer Aided Design
JF - CAD Computer Aided Design
SN - 0010-4485
IS - 3
ER -