{"id":2218,"date":"2021-08-31T13:03:53","date_gmt":"2021-08-31T13:03:53","guid":{"rendered":"http:\/\/sites.uac.pt\/amendes\/?p=2218"},"modified":"2021-08-31T13:03:53","modified_gmt":"2021-08-31T13:03:53","slug":"repulsive-curves","status":"publish","type":"post","link":"https:\/\/sites.uac.pt\/amendes\/visualizacao\/repulsive-curves\/","title":{"rendered":"Repulsive Curves"},"content":{"rendered":"\n<div class=\"wp-block-cover has-background-dim\" style=\"min-height:145px;aspect-ratio:unset;\"><img decoding=\"async\" class=\"wp-block-cover__image-background\" alt=\"\" src=\"http:\/\/www.cs.cmu.edu\/~kmcrane\/Projects\/RepulsiveCurves\/teaser.png\" data-object-fit=\"cover\" \/><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-large-font-size\"><a href=\"http:\/\/www.cs.cmu.edu\/~kmcrane\/Projects\/RepulsiveCurves\/index.html\" data-type=\"URL\" data-id=\"http:\/\/www.cs.cmu.edu\/~kmcrane\/Projects\/RepulsiveCurves\/index.html\">Clique para seguir o link<\/a><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-luminous-vivid-amber-color has-text-color\">Um trabalho muito interessante e com muito c\u00f3digo sobre os melhores algoritmos para construir curvas que n\u00e3o se sobrep\u00f5em<\/p>\n\n\n\n<p>Curves play a fundamental role across computer graphics, physical simulation, and mathematical visualization, yet most tools for curve design do nothing to prevent crossings or self-intersections. This paper develops efficient algorithms for (self-)repulsion of plane and space curves that are well-suited to problems in computational design. Our starting point is the so-called\u00a0<em>tangent-point energy<\/em>, which provides an infinite barrier to self-intersection. In contrast to local collision detection strategies used in,\u00a0<em>e.g.<\/em>, physical simulation, this energy considers interactions between all pairs of points, and is hence useful for global shape optimization: local minima tend to be aesthetically pleasing, physically valid, and nicely distributed in space. A reformulation of gradient descent, based on a\u00a0<em>Sobolev-Slobodeckij inner product<\/em>\u00a0enables us to make rapid progress toward local minima\u2014independent of curve resolution. We also develop a hierarchical multigrid scheme that significantly reduces the per-step cost of optimization. The energy is easily integrated with a variety of constraints and penalties (<em>e.g.<\/em>, inextensibility, or obstacle avoidance), which we use for applications including curve packing, knot untangling, graph embedding, non-crossing spline interpolation, flow visualization, and robotic path planning.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Um trabalho muito interessante e com muito c\u00f3digo sobre os melhores algoritmos para construir curvas que n\u00e3o se sobrep\u00f5em Curves play a fundamental role across computer graphics, physical simulation, and mathematical visualization, yet most tools for curve design do nothing to prevent crossings or self-intersections. This paper develops efficient algorithms for (self-)repulsion of plane and [&hellip;]<\/p>\n","protected":false},"author":159,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[150,136,80],"tags":[4151,108,4061],"class_list":["post-2218","post","type-post","status-publish","format-standard","hentry","category-materiais-para-profissionais","category-refs-bibliograficas","category-visualizacao","tag-curvas","tag-grafos","tag-graphs"],"_links":{"self":[{"href":"https:\/\/sites.uac.pt\/amendes\/wp-json\/wp\/v2\/posts\/2218","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.uac.pt\/amendes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.uac.pt\/amendes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.uac.pt\/amendes\/wp-json\/wp\/v2\/users\/159"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.uac.pt\/amendes\/wp-json\/wp\/v2\/comments?post=2218"}],"version-history":[{"count":1,"href":"https:\/\/sites.uac.pt\/amendes\/wp-json\/wp\/v2\/posts\/2218\/revisions"}],"predecessor-version":[{"id":2219,"href":"https:\/\/sites.uac.pt\/amendes\/wp-json\/wp\/v2\/posts\/2218\/revisions\/2219"}],"wp:attachment":[{"href":"https:\/\/sites.uac.pt\/amendes\/wp-json\/wp\/v2\/media?parent=2218"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.uac.pt\/amendes\/wp-json\/wp\/v2\/categories?post=2218"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.uac.pt\/amendes\/wp-json\/wp\/v2\/tags?post=2218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}