Freeform Geometric Models Yong-Joon Kim, Myung-Soo Kim (Seoul - PowerPoint PPT Presentation

Jul 23, 2023 •210 likes •510 views

Efficient Algorithms for Freeform Geometric Models Yong-Joon Kim, Myung-Soo Kim (Seoul National University) Gershon Elber (Technion, Israel) Collision Detection Collision Detection Minimum Distance Hausdorff Distance Convex Hull

Efficient Algorithms for Freeform Geometric Models Yong-Joon Kim, Myung-Soo Kim (Seoul National University) Gershon Elber (Technion, Israel)
Collision Detection
Collision Detection
Minimum Distance
Hausdorff Distance
Convex Hull Computation
Previous Approach
Problem Reduction to (u,v) • The bisector curve of C(u) and D(v) is reduced to solving F(u,v)=0. • Much lower degree than the bisector curve b(x,y)=0 itself in the xy-plane. • Many other geometric problems can be solved in a similar way. • But, this approach is too slow. => Preprocessing is needed!!!
Preprocessing for Freeforms • Biarc approximation of planar curves • Segmentation of planar curves to monotone spiral curves • Support distance functions • Approximation with simple surfaces
Background • IK Bi-National Grant (2007-2009) - Hausdorff distance computation for freeform curves and surfaces • Tang, Lee, and Kim (SIGGRAPH 2009) - Real-time HD computation for triangular meshes using BVH (prebuilt hierarchical data structure)
Bounding Volume Hierarchy
View Frustum Culling
Conventional Bounding Volume
Conventional BVH Complexity (Yoon and Manocha, EG2006)
Coons Patch
Approx. with Coons Patches
Approx. with Coons Patches
Bounding Coons Patches
Two Steps of Approximation • Bezier surface by Coons patches ( ) • Coons patch by bilinear surfaces ( ) by approximating the boundary curves Bounding Volume • Bounding bilinear surface by tetrahedron and offset by maximum error
Bounding Coons Patches
Comparison
BVH Complexity
BVH Complexity
BVH Complexity
BVH Complexity
Performance Comparison
Performance Comparison
Conclusions • Compact BVH for Freefrom Models • Efficient Geometric Algorithms - Collision detection - Minimum distance computation - Hausdorff distance computation - Convex hull computation

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