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A null-object detection algorithm for constructive solid geometry

Author:

Robert B. TiloveAuthors Info & Claims

Communications of the ACM, Volume 27, Issue 7

Pages 684 - 694

https://doi.org/10.1145/358105.358195

Published: 01 July 1984 Publication History

Abstract

Constructive solid geometry (CSG) is the primary scheme used for representing solid objects in many contemporary solid modeling systems. A CSG representation is a binary tree whose nonterminal nodes represent Boolean operations and whose terminal nodes represent primitive solids. This paper deals with algorithms that operate directly on CSG representations to solve two computationally difficult geometric problems—null-object detection (NOD) and same-object detection (SOD). The paper also shows that CSG trees representing null objects may be reduced to null trees through the use of a new concept called primitive redundancy, and that, on average, tree reduction can be done efficiently by a new technique called spatial localization. Primitive redundancy and spatial localization enable a single complex instance of NOD to be converted into a number of simpler subproblems and lead to more efficient algorithms than those previously known.

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Tilove, R.B. Exploiting spatial and structural locality in geometric modelling. Ph.D. dissertation, Dept. of Electrical Engineering, Univ. of Rochester, Rochester, NY, October 1981. (Available as Tech. Memo. 38, Production Automation Project, Univ. of Rochester, Rochester, NY}, October 1981.

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Cited By

Liu HAgrawala MYuksel COmernick TMisra VCorazza SMcguire MZordan V(2024)A Unified Differentiable Boolean Operator with Fuzzy LogicACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657484(1-9)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657484
Fayolle PFriedrich M(2024)A Survey of Methods for Converting Unstructured Data to CSG ModelsComputer-Aided Design10.1016/j.cad.2023.103655168(103655)Online publication date: Mar-2024
https://doi.org/10.1016/j.cad.2023.103655
Kurzeja KRossignac J(2022)CTSPComputer-Aided Design10.1016/j.cad.2022.103212146:COnline publication date: 1-May-2022
https://dl.acm.org/doi/10.1016/j.cad.2022.103212
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Index Terms

A null-object detection algorithm for constructive solid geometry
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Volumetric models
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Reviews

Reviewer: Frances Akridge

This paper introduces an algorithm that operates directly on CSG representations to solve two computationally difficult geometric problems: Null-Object Detection (NOD) and Same-Object Detection (SOD). The algorithm, which focuses on NOD, exploits two new concepts—primitive redundancy and spatial localization—which, although not precisely defined, are explained by two- and three-dimensional examples. The computational complexity of the algorithm is not formally analyzed. However, it purports to be superior to the traditional algorithms in cases where nullness is expected. The paper is taken from Tilove's PhD dissertation [1].

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Published In

cover image Communications of the ACM

Communications of the ACM Volume 27, Issue 7

July 1984

96 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/358105

Editor:
Peter J. Denning
NASA Ames Research Center, Moffett Field, CA

Issue’s Table of Contents

Copyright © 1984 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1984

Published in CACM Volume 27, Issue 7

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Cited By

Liu HAgrawala MYuksel COmernick TMisra VCorazza SMcguire MZordan V(2024)A Unified Differentiable Boolean Operator with Fuzzy LogicACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657484(1-9)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657484
Fayolle PFriedrich M(2024)A Survey of Methods for Converting Unstructured Data to CSG ModelsComputer-Aided Design10.1016/j.cad.2023.103655168(103655)Online publication date: Mar-2024
https://doi.org/10.1016/j.cad.2023.103655
Kurzeja KRossignac J(2022)CTSPComputer-Aided Design10.1016/j.cad.2022.103212146:COnline publication date: 1-May-2022
https://dl.acm.org/doi/10.1016/j.cad.2022.103212
Cox WWhile LReynolds M(2021)A Review of Methods to Compute Minkowski Operations for Geometric Overlap DetectionIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2020.297692227:8(3377-3396)Online publication date: 1-Aug-2021
https://dl.acm.org/doi/10.1109/TVCG.2020.2976922
Cameron S(2016)Efficient Intersection Tests for Objects Defined ConstructivelyThe International Journal of Robotics Research10.1177/0278364989008001018:1(3-25)Online publication date: 2-Jul-2016
https://doi.org/10.1177/027836498900800101
Fryazinov OPasko A(2015)Reliable detection and separation of components for solid objects defined with scalar fieldsComputer-Aided Design10.1016/j.cad.2014.08.01958:C(43-50)Online publication date: 1-Jan-2015
https://dl.acm.org/doi/10.1016/j.cad.2014.08.019
Lysenko M(2013)Fourier collision detectionInternational Journal of Robotics Research10.1177/027836491347716532:4(483-503)Online publication date: 1-Apr-2013
https://dl.acm.org/doi/10.1177/0278364913477165
Odendahl SKersting P(2013)Higher Efficiency Modeling of Surface Location Errors by Using a Multi-scale Milling SimulationProcedia CIRP10.1016/j.procir.2013.06.1619(18-22)Online publication date: 2013
https://doi.org/10.1016/j.procir.2013.06.161
Lee SLee K(2012)Simultaneous and incremental feature-based multiresolution modeling with feature operations in part designComputer-Aided Design10.1016/j.cad.2011.12.00544:5(457-483)Online publication date: 1-May-2012
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Lysenko MD'Souza RShene C(2008)Improved Binary Space Partition mergingComputer-Aided Design10.1016/j.cad.2008.11.00240:12(1113-1120)Online publication date: 1-Dec-2008
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