SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Interval methods for multi-point collisions between time-dependent curved surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs
IEEE Transactions on Visualization and Computer Graphics
Distance Computation between Non-Convex Polyhedra at Short Range Based on Discrete Voronoi Regions
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
A Scan Line Algorithm for Rendering Curved Tubular Objects
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
Computing Distances between Surfaces Using Line Geometry
PG '02 Proceedings of the 10th Pacific Conference on Computer Graphics and Applications
Shrinking: Another Method for Surface Reconstruction
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
Clifford algebra, Lorentzian geometry, and rational parametrization of canal surfaces
Computer Aided Geometric Design
Minimum distance between two sphere-swept surfaces
Computer-Aided Design
Almost rotation-minimizing rational parametrization of canal surfaces
Computer Aided Geometric Design
Computing minimum distance between two implicit algebraic surfaces
Computer-Aided Design
Robustly computing intersection curves of two canal surfaces with quadric decomposition
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
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A canal surface is the envelope of a one-parameter set of moving spheres. We present an accurate and efficient method for computing the distance between two canal surfaces. First, we use a set of cone-spheres to enclose a canal surface. A cone-sphere is a surface generated by sweeping a sphere along a straight line segment with the radius of the sphere changing linearly; thus it is a truncated circular cone capped by spheres at the two ends. Then, for two canal surfaces we use the distances between their bounding cone-spheres to approximate their distance; the accuracy of this approximation is improved by subdividing the canal surfaces into more segments and use more cone-spheres to bound the segments, until a pre-specified threshold is reached. We present a method for computing tight bounding cone-spheres of a canal surface, which is an interesting problem in its own right. Based on it, we present a complete method for efficiently computing the distances between two canal surfaces using the distances among all pairs of their bounding cone-spheres. The key to its efficiency is a novel pruning technique that can eliminate most of the pairs of cone-spheres that do not contribute to the distance between the original canal surfaces. Experimental comparisons show that our method is more efficient than Lee et al's method [13] for computing the distance between two complex objects composed of many canal surfaces.