In this paper, we propose a simple-yet-effective method for isotropic meshing relying on Euclidean distance transformation based centroidal Voronoi tessellation (CVT). Our approach improves the performance and robustness of computing CVT on curved domains while simultaneously providing high-quality output meshes. While conventional extrinsic methods compute CVTs in the entire volume bounded by the input model, we restrict the computation to a 3D shell of user-controlled thickness. Taking voxels which contain surface samples as sites, we compute the exact Euclidean distance transform on the GPU. Our algorithm is parallel and memory-efficient, and can construct the shell space for resolutions up to 2048 3 at interactive speed. The 3D centroidal Voronoi tessellation and restricted Voronoi diagrams are also computed efficiently on the GPU. Since the shell space can bridge holes and gaps smaller than a certain tolerance, and tolerate non-manifold edges and degenerate triangles, our algorithm can handle models with such defects, which typically cause conventional remeshing methods to fail. Our method can process implicit surfaces, polyhedral surfaces, and point clouds in a unified framework. Computational results show that our GPU-based isotropic meshing algorithm produces results comparable to state-of- the-art techniques, but is significantly faster than conventional CPU-based implementations.

Abstract Piecewise linear polygonal model has onlyG0continuity, thus users can easily feel the edges when using haptic device to touch a solid represented by coarse polygonal meshes. To produce an appealing haptic sensation for smooth solids, a large number of polygons are needed in conventional approaches. This, however, slows down computation and consumes much more memory. In this paper, we present a method to generate smooth feedback force in haptic interaction with coarse polygonal meshes. Our method calculates the interaction force based on Gregory patches, which are locally constructed fromn‐sided polygons and ensureG1continuity across boundaries of patches. During the real time haptic interaction, the contact point is continuously tracked on the locally constructed Gregory patches and thus generates smooth haptic forces to be rendered. Our method is validated on various models with comparison to conventional force rendering techniques. Copyright © 2010 John Wiley & Sons, Ltd.