## A unified approach for physically-based simulations and haptic rendering

- René Weller, Gabriel Zachmann
- Sandbox '09
- 2009

@article{Schrcker2014GuaranteedCD, title={Guaranteed Collision Detection With Toleranced Motions}, author={Hans-Peter Schr{\"o}cker and Matthias J. Weber}, journal={Computer Aided Geometric Design}, year={2014}, volume={31}, pages={602-612} }

- Published 2014 in Computer Aided Geometric Design
DOI:10.1016/j.cagd.2014.08.001

We present a method for guaranteed collision detection with toleranced motions. The basic idea is to consider the motion as a curve in the 12-dimensional space of affine displacements, endowed with an object-oriented Euclidean metric, and cover it with balls. The associated orbits of points, lines, planes and polygons have particularly simple shapes that lend themselves well to exact and fast collision queries. We present formulas for elementary collision tests with these orbit shapes and we… CONTINUE READING