Be´zier curves and surface patches on quadrics
Mathematical methods in computer aided geometric design II
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
The bisector surface of freeform rational space curves
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
GAPS: general and automatic polygonal simplification
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
Efficient Distance Computation for Quadratic Curves and Surfaces
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Efficient Computation of the Hausdorff Distance Between Polytopes by Exterior Random Covering
Computational Optimization and Applications
Minimum distance queries for haptic rendering
Minimum distance queries for haptic rendering
Interactive Hausdorff distance computation for general polygonal models
ACM SIGGRAPH 2009 papers
Computing the minimum distance between two Bézier curves
Journal of Computational and Applied Mathematics
Computing minimum distance between two implicit algebraic surfaces
Computer-Aided Design
Hausdorff and minimal distances between parametric freeforms in R2and R3
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Precise Hausdorff distance computation for planar freeform curves using biarcs and depth buffer
The Visual Computer: International Journal of Computer Graphics
Polyline approach for approximating Hausdorff distance between planar free-form curves
Computer-Aided Design
GPU-accelerated Hausdorff distance computation between dynamic deformable NURBS surfaces
Computer-Aided Design
Efficient point-projection to freeform curves and surfaces
Computer Aided Geometric Design
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We present an exact algorithm for computing the precise Hausdorff distance between two general polyhedra represented as triangular meshes. The locus of candidate points, events where the Hausdorff distance may occur, is fully classified. These events include simple cases where foot points of vertices are examined as well as more complicated cases where extreme distance evaluation is needed on the intersection curve of one mesh with the medial axis of the other mesh. No explicit reconstruction of the medial axis is conducted and only bisectors of pairs of primitives (i.e. vertex, edge, or face) are analytically constructed and intersected with the other mesh, yielding a set of conic segments. For each conic segment, the distance functions to all primitives are constructed and the maximum value of their low envelope function may correspond to a candidate point for the Hausdorff distance. The algorithm is fully implemented and several experimental results are also presented.