{"id":605,"date":"2009-09-16T16:17:08","date_gmt":"2009-09-16T21:17:08","guid":{"rendered":"https:\/\/Engineering.Purdue.edu\/precisetest\/wp\/?p=605"},"modified":"2015-08-02T22:23:32","modified_gmt":"2015-08-03T03:23:32","slug":"computing-global-visibility-maps-for-regions-on-the-boundaries-of-polyhedra-using-minkowski-sums","status":"publish","type":"post","link":"https:\/\/engineering.purdue.edu\/cdesign\/wp\/computing-global-visibility-maps-for-regions-on-the-boundaries-of-polyhedra-using-minkowski-sums\/","title":{"rendered":"Computing global visibility maps for regions on the boundaries of polyhedra using Minkowski sums"},"content":{"rendered":"<h2 id=\"section_abstract\"><em>Abstract<\/em><\/h2>\n<p>A global visibility map is a spherical image built to describe the complete set of global visible view directions for a surface. In this paper, we consider the computation of global visibility maps for regions on the boundary of a polyhedron. Both the self-occlusions introduced by a region and the global occlusions introduced by the rest of the surfaces on the boundary of the polyhedron are considered for computing a global visibility map. We show that the occluded view directions introduced between a pair of polyhedral surfaces can be computed from the spherical projection of the Minkowski sum of one surface and the reflection of the other. A suitable subset of the Minkowski sum, which shares the identical spherical projection with the complete Minkowski sum, is constructed to obtain the spherical images representing global occlusions. Our method has been successfully tested on many CAD models. It extends the previous methods for computing global visibility maps using convex decomposition, and it exhibits a better performance.<\/p>\n<p><a href=\"https:\/\/Engineering.Purdue.edu\/precisetest\/wp\/wp-content\/uploads\/2012\/05\/spm_min.jpg\"><img loading=\"lazy\" class=\"alignnone size-full wp-image-694\" title=\"spm_min\" src=\"https:\/\/Engineering.Purdue.edu\/precisetest\/wp\/wp-content\/uploads\/2012\/05\/spm_min.jpg\" alt=\"\" width=\"357\" height=\"188\" srcset=\"https:\/\/engineering.purdue.edu\/cdesign\/wp\/wp-content\/uploads\/2012\/05\/spm_min.jpg 357w, https:\/\/engineering.purdue.edu\/cdesign\/wp\/wp-content\/uploads\/2012\/05\/spm_min-300x158.jpg 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/a><\/p>\n<pre><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Abstract A global visibility map is a spherical image built to describe the complete set of global visible view directions for a surface. In this paper, we consider the computation of global visibility maps for regions on the boundary of a polyhedron. Both the self-occlusions introduced by a region and the global occlusions introduced by [&hellip;]<\/p>\n","protected":false},"author":15,"featured_media":694,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","_links_to":"","_links_to_target":""},"categories":[52,282,8,286],"tags":[288,168,167,169,323,170,351],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Computing global visibility maps for regions on the boundaries of polyhedra using Minkowski sums - Convergence Design Lab, Purdue University<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/engineering.purdue.edu\/cdesign\/wp\/computing-global-visibility-maps-for-regions-on-the-boundaries-of-polyhedra-using-minkowski-sums\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Computing global visibility maps for regions on the boundaries of polyhedra using Minkowski sums - Convergence Design Lab, Purdue University\" \/>\n<meta property=\"og:description\" content=\"Abstract A global visibility map is a spherical image built to describe the complete set of global visible view directions for a surface. In this paper, we consider the computation of global visibility maps for regions on the boundary of a polyhedron. Both the self-occlusions introduced by a region and the global occlusions introduced by [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/engineering.purdue.edu\/cdesign\/wp\/computing-global-visibility-maps-for-regions-on-the-boundaries-of-polyhedra-using-minkowski-sums\/\" \/>\n<meta property=\"og:site_name\" content=\"Convergence Design Lab, Purdue University\" \/>\n<meta property=\"article:published_time\" content=\"2009-09-16T21:17:08+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2015-08-03T03:23:32+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/engineering.purdue.edu\/cdesign\/wp\/wp-content\/uploads\/2012\/05\/spm_min.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"357\" \/>\n\t<meta property=\"og:image:height\" content=\"188\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"_not_Exist_\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/engineering.purdue.edu\/cdesign\/wp\/#organization\",\"name\":\"Convergence Design Lab - 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