Approximate conversion of spline curves
Computer Aided Geometric Design - Special issue: Topics in CAGD
Loop detection in surface patch intersections
Computer Aided Geometric Design
Second-order surface analysis using hybrid symbolic and numeric operators
ACM Transactions on Graphics (TOG)
Numerical analysis: mathematics of scientific computing (2nd ed)
Numerical analysis: mathematics of scientific computing (2nd ed)
Point inversion and projection for NURBS curve and surface: control polygon approach
Computer Aided Geometric Design
Efficient Computation of the Hausdorff Distance Between Polytopes by Exterior Random Covering
Computational Optimization and Applications
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
A second order algorithm for orthogonal projection onto curves and surfaces
Computer Aided Geometric Design
Optimized GPU evaluation of arbitrary degree NURBS curves and 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 between polygonal meshes
Computer Aided Geometric Design
Coons BVH for freeform geometric models
Proceedings of the 2011 SIGGRAPH Asia Conference
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We present a GPU algorithm for computing the directed Hausdorff distance between two NURBS surfaces. The algorithm is based on sampling of one surface, and performing numerical iterations on the GPU to compute the minimal distance from each sample to the other surface. An error analysis for the Hausdorff distance computations is performed, based on bounds on the NURBS surfaces. We compare a CUDA implementation of our algorithm to existing methods, demonstrating that the new method addresses limitations of previous hierarchical culling methods such as the sensitivity to the position of the inputs.