Surface algorithms using bounds on derivatives
Computer Aided Geometric Design
Accurate Minkowski sum approximation of polyhedral models
Graphical Models - Special issue on PG2004
Interactive Hausdorff distance computation for general polygonal models
ACM SIGGRAPH 2009 papers
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
Precise Hausdorff distance computation between polygonal meshes
Computer Aided Geometric Design
Computing the Hausdorff distance between two B-spline curves
Computer-Aided Design
Polyline approach for approximating Hausdorff distance between planar free-form curves
Computer-Aided Design
Coons BVH for freeform geometric models
Proceedings of the 2011 SIGGRAPH Asia Conference
GPU-accelerated Hausdorff distance computation between dynamic deformable NURBS surfaces
Computer-Aided Design
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We present an interactive-speed algorithm for computing the Hausdorff Distance (HD) between two freeform geometric models represented with NURBS surfaces. The algorithm is based on an effective technique for matching a surface patch from one model to the corresponding nearby surface patch on the other model. To facilitate the matching procedure, we employ a bounding volume hierarchy (BVH) for freeform NURBS surfaces, which provides a hierarchy of Coons patches and bilinear surfaces approximating the NURBS surfaces (Kim et al., 2011 [1]). Comparing the local HD upper bound against a global HD lower bound, we can eliminate the majority of redundant surface patches from further consideration. The resulting algorithm and the associated data structures are considerably simpler than the previous BVH-based HD algorithms. As a result, we can compute the HD of two freeform geometric models efficiently and robustly even when the two models are in close proximity. We demonstrate the effectiveness of our approach using several experimental results.