Robust cascading of operations on polyhedra

Elisha Sacks; Victor Milenkovic

doi:10.1016/j.cad.2013.08.035

Robust cascading of operations on polyhedra

Elisha Sacks, Victor Milenkovic

Computer Science

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 language	English (US)
Pages (from-to)	216-220
Number of pages	5
Journal	CAD Computer Aided Design
Volume	46
Issue number	1
DOIs	https://doi.org/10.1016/j.cad.2013.08.035
State	Published - 2014

Keywords

Geometric rounding
Robust computational geometry

ASJC Scopus subject areas

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

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10.1016/j.cad.2013.08.035

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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",

note = "Funding Information: Sacks is supported by NSF grant CCF-0904832 . Milenkovic is supported by NSF grant CCF-0904707 . ",

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AU - Milenkovic, Victor

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PY - 2014

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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

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