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  Boolean Operations on 3D Selective Nef Complexes: Optimized Implementation and Experiments

Hachenberger, P., & Kettner, L. (2005). Boolean Operations on 3D Selective Nef Complexes: Optimized Implementation and Experiments. In ACM Symposium on Solid and Physical Modeling (SPM 2005) (pp. 163-174). New York, USA: ACM.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-25FA-1 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-25FB-0
Genre: Conference Paper

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 Creators:
Hachenberger, Peter1, Author           
Kettner, Lutz1, Author           
Kobbelt, Leif, Editor
Shapiro, Vadim, Editor
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: Nef polyhedra in $d$-dimensional space are the closure of half-spaces under boolean set operation. In consequence, they can represent non-manifold situations, open and closed sets, mixed-dimensional complexes and they are closed under all boolean and topological operations, such as complement and boundary. They were introduced by W. Nef in his seminal 1978 book on polyhedra. We presented in previous work a new data structure for the boundary representation of three-dimensional Nef polyhedra with efficient algorithms for boolean operations. These algorithms were designed for correctness and can handle all cases, in particular all \emph{degeneracies}. To this extent we rely on exact arithmetic to avoid well known problems with floating-point arithmetic. In this paper, we present important optimizations for the algorithms. We describe the chosen implementations for the point-location and the intersection-finding subroutines, a kd-tree and a fast box-intersection algorithm, respectively. We evaluate this optimized implementation with extensive experiments that supplement the runtime analysis from our previous paper and that illustrate the effectiveness of our optimizations. We compare our implementation with the \textsc{Acis} CAD kernel and demonstrate the power and cost of the exact arithmetic in near-degenerate situations. The implementation was released as Open Source in the \textsc{Cgal} release 3.1 in December 2004.

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Language(s): eng - English
 Dates: 2006-01-132005
 Publication Status: Issued
 Pages: -
 Publishing info: New York, USA : ACM
 Table of Contents: -
 Rev. Type: -
 Identifiers: eDoc: 279193
Other: Local-ID: C1256428004B93B8-6DBA4898294F9C69C1256FC50081FC75-HachenbergerKettner2005Nef
 Degree: -

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Title: Untitled Event
Place of Event: Cambridge, MA, USA
Start-/End Date: 2005-06-13

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Title: ACM Symposium on Solid and Physical Modeling (SPM 2005)
Source Genre: Proceedings
 Creator(s):
Affiliations:
Publ. Info: New York, USA : ACM
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 163 - 174 Identifier: ISBN: 1-59593-015-9