Robust polygon modelling

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

The paper provides a set of algorithms for performing set operations on polygonal regions in the plane using standard floating-point arithmetic. The algorithms are robust, guaranteeing both topological consistency and numerical accuracy. Each polygon edge is modelled as an implicit or explicit polygonal curve which stays within some distance ß of the original line segment. If the curve is implicit, ß is bounded by a small multiple of the rounding unit. If the curves are explicit, the bound on ß may grow with the number of curves. One can mix implicit and explicit representations to suit the application.

Original languageEnglish (US)
Pages (from-to)546-566
Number of pages21
JournalCAD Computer Aided Design
Volume25
Issue number9
DOIs
StatePublished - 1993
Externally publishedYes

Fingerprint

Polygon
Digital arithmetic
Curve
Modeling
Floating-point Arithmetic
Numerical Accuracy
Rounding
Line segment
Unit

Keywords

  • algorithms
  • geometric modelling
  • polygons

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering
  • Geometry and Topology

Cite this

Robust polygon modelling. / Milenkovic, Victor.

In: CAD Computer Aided Design, Vol. 25, No. 9, 1993, p. 546-566.

Research output: Contribution to journalArticle

Milenkovic, Victor. / Robust polygon modelling. In: CAD Computer Aided Design. 1993 ; Vol. 25, No. 9. pp. 546-566.
@article{a8b153e1412d429baa66c33b8f9d0db8,
title = "Robust polygon modelling",
abstract = "The paper provides a set of algorithms for performing set operations on polygonal regions in the plane using standard floating-point arithmetic. The algorithms are robust, guaranteeing both topological consistency and numerical accuracy. Each polygon edge is modelled as an implicit or explicit polygonal curve which stays within some distance {\ss} of the original line segment. If the curve is implicit, {\ss} is bounded by a small multiple of the rounding unit. If the curves are explicit, the bound on {\ss} may grow with the number of curves. One can mix implicit and explicit representations to suit the application.",
keywords = "algorithms, geometric modelling, polygons",
author = "Victor Milenkovic",
year = "1993",
doi = "10.1016/0010-4485(93)90071-U",
language = "English (US)",
volume = "25",
pages = "546--566",
journal = "CAD Computer Aided Design",
issn = "0010-4485",
publisher = "Elsevier Limited",
number = "9",

}

TY - JOUR

T1 - Robust polygon modelling

AU - Milenkovic, Victor

PY - 1993

Y1 - 1993

N2 - The paper provides a set of algorithms for performing set operations on polygonal regions in the plane using standard floating-point arithmetic. The algorithms are robust, guaranteeing both topological consistency and numerical accuracy. Each polygon edge is modelled as an implicit or explicit polygonal curve which stays within some distance ß of the original line segment. If the curve is implicit, ß is bounded by a small multiple of the rounding unit. If the curves are explicit, the bound on ß may grow with the number of curves. One can mix implicit and explicit representations to suit the application.

AB - The paper provides a set of algorithms for performing set operations on polygonal regions in the plane using standard floating-point arithmetic. The algorithms are robust, guaranteeing both topological consistency and numerical accuracy. Each polygon edge is modelled as an implicit or explicit polygonal curve which stays within some distance ß of the original line segment. If the curve is implicit, ß is bounded by a small multiple of the rounding unit. If the curves are explicit, the bound on ß may grow with the number of curves. One can mix implicit and explicit representations to suit the application.

KW - algorithms

KW - geometric modelling

KW - polygons

UR - http://www.scopus.com/inward/record.url?scp=0027663954&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027663954&partnerID=8YFLogxK

U2 - 10.1016/0010-4485(93)90071-U

DO - 10.1016/0010-4485(93)90071-U

M3 - Article

AN - SCOPUS:0027663954

VL - 25

SP - 546

EP - 566

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

SN - 0010-4485

IS - 9

ER -