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<p><b>Abstract</b>—We introduce a new algorithm for computing the distance from a point to an arbitrary polygonal mesh. Our algorithm uses a multiresolution hierarchy of bounding volumes generated by geometric simplification. Our algorithm is dynamic, exploiting coherence between subsequent queries using a priority process and achieving constant time queries in some cases. It can be applied to meshes that transform rigidly or deform nonrigidly. We illustrate our algorithm with a simulation of particle dynamics and collisions with a deformable mesh, the computation of distance maps and offset surfaces, the computation of an approximation to the expensive Hausdorff distance between two shapes, and the detection of self-intersections. We also report comparison results between our algorithm and an alternative algorithm using an octree, upon which our method permits an order-of-magnitude speed-up.</p>
Triangular mesh, closest point, multiresolution hierarchy, priority process, dynamic queries.
André Guéziec, "'Meshsweeper': Dynamic Point-to-Polygonal-Mesh Distance and Applications", IEEE Transactions on Visualization & Computer Graphics, vol. 7, no. , pp. 47-61, January-March 2001, doi:10.1109/2945.910820
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