# 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 language English (US) 216-220 5 CAD Computer Aided Design 46 1 https://doi.org/10.1016/j.cad.2013.08.035 Published - 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.
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