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 | |
| State | Published - Jan 1 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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Cite this
Sacks, E., & Milenkovic, V. (2014). Robust cascading of operations on polyhedra. CAD Computer Aided Design, 46(1), 216-220. https://doi.org/10.1016/j.cad.2013.08.035