Surface algorithms using bounds on derivatives
Computer Aided Geometric Design
Efficient Computation of the Hausdorff Distance Between Polytopes by Exterior Random Covering
Computational Optimization and Applications
GPU-based trimming and tessellation of NURBS and T-Spline surfaces
ACM SIGGRAPH 2005 Papers
Accurate Minkowski sum approximation of polyhedral models
Graphical Models - Special issue on PG2004
Scan primitives for GPU computing
Proceedings of the 22nd ACM SIGGRAPH/EUROGRAPHICS symposium on Graphics hardware
Interactive Hausdorff distance computation for general polygonal models
ACM SIGGRAPH 2009 papers
Accelerating geometric queries using the GPU
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
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
| Hi-index | 0.00 |
We present a parallel GPU-accelerated algorithm for computing the directed Hausdorff distance from one NURBS surface to another, within a bound. We make use of axis-aligned bounding-box hierarchies that bound the NURBS surfaces to accelerate the computations. We dynamically construct as well as traverse the bounding-box hierarchies for the NURBS surfaces using operations that are optimized for the GPU. To compute the Hausdorff distance, we traverse this hierarchy after culling bounding-box pairs that do not contribute to the Hausdorff distance. Our contribution includes two-sided culling tests that can be performed in parallel using the GPU. The culling, based on the minimum and maximum distance ranges between the bounding boxes, eliminates bounding-box pairs from both surfaces that do not contribute to the Hausdorff distance simultaneously. We calculate accuracy bounds for our computed Hausdorff distance based on the curvature of the surfaces. Our algorithm runs in real-time with very small guaranteed error bounds for complex NURBS surfaces. Since we dynamically construct our bounding-box hierarchy, our algorithm can be used to interactively compute the Hausdorff distance for models made of dynamic deformable surfaces.