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 - 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 journal › Article
}
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 -