{"id":8082,"date":"2012-08-18T15:01:47","date_gmt":"2012-08-18T12:01:47","guid":{"rendered":"http:\/\/hgpu.org\/?p=8082"},"modified":"2012-08-18T15:01:47","modified_gmt":"2012-08-18T12:01:47","slug":"gpu-based-computation-of-discrete-periodic-centroidal-voronoi-tessellation-in-hyperbolic-space","status":"publish","type":"post","link":"https:\/\/hgpu.org\/?p=8082","title":{"rendered":"GPU-Based Computation of Discrete Periodic Centroidal Voronoi Tessellation in Hyperbolic Space"},"content":{"rendered":"<p>Periodic centroidal Voronoi tessellation (CVT) in hyperbolic space provides a nice theoretical framework for computing the constrained CVT on high-genus (genus &gt; 1) surfaces. This paper addresses two computational issues related to such hyperbolic CVT framework: (1) efficient reduction of unnecessary site copies in neighbor domains on the universal covering space, based on two special rules; (2) GPU-based parallel algorithms to compute a discrete version of the hyperbolic CVT. Our experiments show that with the dramatically reduced number of unnecessary site copies in neighbor domains and the GPU-based parallel algorithms, we significantly speed up the computation of CVT for high-genus surfaces. The proposed discrete hyperbolic CVT guarantees to converge and produces high-quality results.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Periodic centroidal Voronoi tessellation (CVT) in hyperbolic space provides a nice theoretical framework for computing the constrained CVT on high-genus (genus &gt; 1) surfaces. This paper addresses two computational issues related to such hyperbolic CVT framework: (1) efficient reduction of unnecessary site copies in neighbor domains on the universal covering space, based on two special [&hellip;]<\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[180,36,11,89,3],"tags":[1797,1787,1782,14,20,974,866,133],"class_list":["post-8082","post","type-post","status-publish","format-standard","hentry","category-3d-graphics-and-realism","category-algorithms","category-computer-science","category-nvidia-cuda","category-paper","tag-3d-graphics-and-realism","tag-algorithms","tag-computer-science","tag-cuda","tag-nvidia","tag-nvidia-geforce-gtx-580","tag-tessellation","tag-voronoi-diagram"],"views":2833,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/8082","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8082"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/8082\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8082"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8082"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8082"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}