Geometric design of motions constrained by a contacting surface pair
Computer Aided Geometric Design
Journal of Computer Science and Technology - Special issue on computer graphics and computer-aided design
Efficient collision detection for moving ellipsoids using separating planes
Computing - Geometric modelling dagstuhl 2002
Computing minimum distance between two implicit algebraic surfaces
Computer-Aided Design
Oriented bounding surfaces with at most six common normals
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Computing the distance between canal surfaces
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
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We present an algorithm for computing the distance between two free-form surfaces. Using line geometry, the distance computation is reformulated as a simple instance of a surface-surface intersection problem, which leads to low-dimensional root finding in a system of equations. This approach produces an efficient algorithm for computing the distance between two ellipsoids, where the problem is reduced to finding a specific solution in a system of two equations in two variables. Similar algorithms can be designed for computing the distance between an ellipsoid and a simple surface (such as cylinder, cone, or torus). In an experimental implementation (on a 500 MHz Windows PC), the distance between two ellipsoids was computed in less than 0.3 msec on average; and the distance between an ellipsoid and a simple convex surface was computed in less than 0.15 msec on average.