Robust cascading of operations on polyhedra

Elisha Sacks, Victor Milenkovic

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We present a geometric rounding algorithm for robustly implementing cascaded operations on polyhedra where the output of each operation is an input to the next operation. The rounding algorithm reduces the bit-precision of the input and eliminates degeneracy. To do so, it rounds coordinates to floating point and randomly perturbs them, then prunes away invalid portions of the resulting polyhedron. We demonstrate the rounding algorithm on a packing algorithm with ten cascaded Minkowski sums and set operations.

Original languageEnglish (US)
Pages (from-to)216-220
Number of pages5
JournalCAD Computer Aided Design
Volume46
Issue number1
DOIs
StatePublished - 2014

Keywords

  • Geometric rounding
  • Robust computational geometry

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Industrial and Manufacturing Engineering

Cite this

Robust cascading of operations on polyhedra. / Sacks, Elisha; Milenkovic, Victor.

In: CAD Computer Aided Design, Vol. 46, No. 1, 2014, p. 216-220.

Research output: Contribution to journalArticle

Sacks, Elisha ; Milenkovic, Victor. / Robust cascading of operations on polyhedra. In: CAD Computer Aided Design. 2014 ; Vol. 46, No. 1. pp. 216-220.
@article{c39b130ddbc44e7f86494b6a22e05833,
title = "Robust cascading of operations on polyhedra",
abstract = "We present a geometric rounding algorithm for robustly implementing cascaded operations on polyhedra where the output of each operation is an input to the next operation. The rounding algorithm reduces the bit-precision of the input and eliminates degeneracy. To do so, it rounds coordinates to floating point and randomly perturbs them, then prunes away invalid portions of the resulting polyhedron. We demonstrate the rounding algorithm on a packing algorithm with ten cascaded Minkowski sums and set operations.",
keywords = "Geometric rounding, Robust computational geometry",
author = "Elisha Sacks and Victor Milenkovic",
year = "2014",
doi = "10.1016/j.cad.2013.08.035",
language = "English (US)",
volume = "46",
pages = "216--220",
journal = "CAD Computer Aided Design",
issn = "0010-4485",
publisher = "Elsevier Limited",
number = "1",

}

TY - JOUR

T1 - Robust cascading of operations on polyhedra

AU - Sacks, Elisha

AU - Milenkovic, Victor

PY - 2014

Y1 - 2014

N2 - We present a geometric rounding algorithm for robustly implementing cascaded operations on polyhedra where the output of each operation is an input to the next operation. The rounding algorithm reduces the bit-precision of the input and eliminates degeneracy. To do so, it rounds coordinates to floating point and randomly perturbs them, then prunes away invalid portions of the resulting polyhedron. We demonstrate the rounding algorithm on a packing algorithm with ten cascaded Minkowski sums and set operations.

AB - We present a geometric rounding algorithm for robustly implementing cascaded operations on polyhedra where the output of each operation is an input to the next operation. The rounding algorithm reduces the bit-precision of the input and eliminates degeneracy. To do so, it rounds coordinates to floating point and randomly perturbs them, then prunes away invalid portions of the resulting polyhedron. We demonstrate the rounding algorithm on a packing algorithm with ten cascaded Minkowski sums and set operations.

KW - Geometric rounding

KW - Robust computational geometry

UR - http://www.scopus.com/inward/record.url?scp=84887465428&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887465428&partnerID=8YFLogxK

U2 - 10.1016/j.cad.2013.08.035

DO - 10.1016/j.cad.2013.08.035

M3 - Article

AN - SCOPUS:84887465428

VL - 46

SP - 216

EP - 220

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

SN - 0010-4485

IS - 1

ER -