{"id":266763,"date":"2025-06-01T09:24:31","date_gmt":"2025-06-01T09:24:31","guid":{"rendered":"https:\/\/peraltafinancing.com\/animation\/a-robust-and-generalized-gauss-seidel-solver-for-physically-correct-simultaneous-collisions-physics-based-animation\/"},"modified":"2025-06-01T09:24:31","modified_gmt":"2025-06-01T09:24:31","slug":"a-robust-and-generalized-gauss-seidel-solver-for-physically-correct-simultaneous-collisions-physics-based-animation","status":"publish","type":"post","link":"https:\/\/fivemor.com\/?p=266763","title":{"rendered":"A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions \u00bb Physics-Based Animation"},"content":{"rendered":"<p> <br \/>\n<\/p>\n<div id=\"post-4194\">\n<div class=\"itemtext\">\n<p>Huanbo Zhou, Zhenyu Xu, Xijun Liu, Xinyu Zhang<\/p>\n<p>Simulating multi-object collisions in real-time environments remains a significant challenge, particularly when handling simultaneous collisions in a physically accurate manner. Traditional Gauss-Seidel solvers, widely employed in physics engines, often fail to preserve the symmetry and consistency of multi-object interactions that are often observed in physics. In this paper, we present a generalized and robust Gauss-Seidel solver to overcome the difficulties in simultaneous collisions. Using spatial and temporal collision states to classify and resolve constraints, our algorithm ensures correct collision propagation and symmetry, addressing the limitations commonly found in existing solvers. Moreover, our algorithm can mitigate jitters caused by floating-point errors, ensuring smooth and stable collision responses. Our approach demonstrates fast convergence and improved accuracy in scenarios involving complex multi-object collisions.<\/p>\n<p><a href=\"https:\/\/dl.acm.org\/doi\/10.1145\/3728291\">A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions<\/a><\/p>\n<\/p><\/div>\n<div class=\"postinfo\">\n\t\t\t<span class=\"postmeta\">Posted by christopherbatty on <a href=\"https:\/\/www.physicsbasedanimation.com\/2025\/05\/26\/a-robust-and-generalized-gauss-seidel-solver-for-physically-correct-simultaneous-collisions\/\">May 26th, 2025<\/a> <\/span><br \/>\n\t\t\t\t\t\t<span class=\"postcats\">Posted in <a href=\"https:\/\/www.physicsbasedanimation.com\/category\/uncategorized\/\" rel=\"category tag\">Uncategorized<\/a><\/span><br \/>\n\t\t\t\t\t\t\t\t\t<span class=\"posttags\"\/>\n\t\t\t\t<\/div>\n<p>\t\t\t\t\t<!--\n\t\t\t\t<rdf:RDF xmlns:rdf=\"http:\/\/www.w3.org\/1999\/02\/22-rdf-syntax-ns#\"\n\t\t\txmlns:dc=\"http:\/\/purl.org\/dc\/elements\/1.1\/\"\n\t\t\txmlns:trackback=\"http:\/\/madskills.com\/public\/xml\/rss\/module\/trackback\/\">\n\t\t<rdf:Description rdf:about=\"https:\/\/www.physicsbasedanimation.com\/2025\/05\/26\/a-robust-and-generalized-gauss-seidel-solver-for-physically-correct-simultaneous-collisions\/\"\n    dc:identifier=\"https:\/\/www.physicsbasedanimation.com\/2025\/05\/26\/a-robust-and-generalized-gauss-seidel-solver-for-physically-correct-simultaneous-collisions\/\"\n    dc:title=\"A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions\"\n    trackback:ping=\"https:\/\/www.physicsbasedanimation.com\/2025\/05\/26\/a-robust-and-generalized-gauss-seidel-solver-for-physically-correct-simultaneous-collisions\/trackback\/\" \/>\n<\/rdf:RDF>\t\t\t-->\n\t\t<\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Huanbo Zhou, Zhenyu Xu, Xijun Liu, Xinyu Zhang Simulating multi-object collisions in real-time environments remains a significant challenge, particularly when handling simultaneous collisions in a physically accurate manner. Traditional Gauss-Seidel solvers, widely employed in physics engines, often fail to preserve the symmetry and consistency of multi-object interactions that are often observed in physics. In this [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":245146,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12035],"tags":[6119,34227,95413,63566,95414,18075,21460,55335,41364],"dealstore":[],"offerexpiration":[],"class_list":["post-266763","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-animation","tag-animation","tag-collisions","tag-gaussseidel","tag-generalized","tag-physicallycorrect","tag-physicsbased","tag-robust","tag-simultaneous","tag-solver"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions \u00bb Physics-Based Animation - Som2ny Network<\/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:\/\/fivemor.com\/?p=266763\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions \u00bb Physics-Based Animation - Som2ny Network\" \/>\n<meta property=\"og:description\" content=\"Huanbo Zhou, Zhenyu Xu, Xijun Liu, Xinyu Zhang Simulating multi-object collisions in real-time environments remains a significant challenge, particularly when handling simultaneous collisions in a physically accurate manner. Traditional Gauss-Seidel solvers, widely employed in physics engines, often fail to preserve the symmetry and consistency of multi-object interactions that are often observed in physics. In this [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/fivemor.com\/?p=266763\" \/>\n<meta property=\"og:site_name\" content=\"Som2ny Network\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T09:24:31+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/05\/blank.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"200\" \/>\n\t<meta property=\"og:image:height\" content=\"200\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\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\":\"Article\",\"@id\":\"https:\/\/fivemor.com\/?p=266763#article\",\"isPartOf\":{\"@id\":\"https:\/\/fivemor.com\/?p=266763\"},\"author\":{\"name\":\"admin\",\"@id\":\"https:\/\/fivemor.com\/#\/schema\/person\/b85e3c3dc0e1daea076524dc8810c371\"},\"headline\":\"A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions \u00bb Physics-Based Animation\",\"datePublished\":\"2025-06-01T09:24:31+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/fivemor.com\/?p=266763\"},\"wordCount\":161,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/fivemor.com\/#organization\"},\"image\":{\"@id\":\"https:\/\/fivemor.com\/?p=266763#primaryimage\"},\"thumbnailUrl\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/05\/blank.jpg\",\"keywords\":[\"Animation\",\"Collisions\",\"GaussSeidel\",\"Generalized\",\"PhysicallyCorrect\",\"PhysicsBased\",\"Robust\",\"Simultaneous\",\"Solver\"],\"articleSection\":[\"Animation\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/fivemor.com\/?p=266763#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/fivemor.com\/?p=266763\",\"url\":\"https:\/\/fivemor.com\/?p=266763\",\"name\":\"A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions \u00bb Physics-Based Animation - Som2ny Network\",\"isPartOf\":{\"@id\":\"https:\/\/fivemor.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/fivemor.com\/?p=266763#primaryimage\"},\"image\":{\"@id\":\"https:\/\/fivemor.com\/?p=266763#primaryimage\"},\"thumbnailUrl\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/05\/blank.jpg\",\"datePublished\":\"2025-06-01T09:24:31+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/fivemor.com\/?p=266763#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/fivemor.com\/?p=266763\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/fivemor.com\/?p=266763#primaryimage\",\"url\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/05\/blank.jpg\",\"contentUrl\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/05\/blank.jpg\",\"width\":200,\"height\":200},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/fivemor.com\/?p=266763#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/fivemor.com\/?bp_activities=1\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions \u00bb Physics-Based Animation\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/fivemor.com\/#website\",\"url\":\"https:\/\/fivemor.com\/\",\"name\":\"Som2ny Network\",\"description\":\"Daily Deals\",\"publisher\":{\"@id\":\"https:\/\/fivemor.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/fivemor.com\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/fivemor.com\/#organization\",\"name\":\"Som2ny Network\",\"url\":\"https:\/\/fivemor.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/fivemor.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/07\/4a0953c4-logo-300x86-1.png\",\"contentUrl\":\"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/07\/4a0953c4-logo-300x86-1.png\",\"width\":300,\"height\":86,\"caption\":\"Som2ny Network\"},\"image\":{\"@id\":\"https:\/\/fivemor.com\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/fivemor.com\/#\/schema\/person\/b85e3c3dc0e1daea076524dc8810c371\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/fivemor.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/729ae85bf62b9917e93538db2f2688ca?s=96&r=g&default=https%3A%2F%2Ffivemor.com%2Fwp-content%2Fplugins%2Fbuddypress-first-letter-avatar%2Fimages%2Fdefault%2F96%2Flatin_a.png\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/729ae85bf62b9917e93538db2f2688ca?s=96&r=g&default=https%3A%2F%2Ffivemor.com%2Fwp-content%2Fplugins%2Fbuddypress-first-letter-avatar%2Fimages%2Fdefault%2F96%2Flatin_a.png\",\"caption\":\"admin\"},\"sameAs\":[\"https:\/\/fivemor.com\"],\"url\":\"https:\/\/fivemor.com\/?author=1\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions \u00bb Physics-Based Animation - Som2ny Network","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/fivemor.com\/?p=266763","og_locale":"en_US","og_type":"article","og_title":"A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions \u00bb Physics-Based Animation - Som2ny Network","og_description":"Huanbo Zhou, Zhenyu Xu, Xijun Liu, Xinyu Zhang Simulating multi-object collisions in real-time environments remains a significant challenge, particularly when handling simultaneous collisions in a physically accurate manner. Traditional Gauss-Seidel solvers, widely employed in physics engines, often fail to preserve the symmetry and consistency of multi-object interactions that are often observed in physics. In this [&hellip;]","og_url":"https:\/\/fivemor.com\/?p=266763","og_site_name":"Som2ny Network","article_published_time":"2025-06-01T09:24:31+00:00","og_image":[{"width":200,"height":200,"url":"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/05\/blank.jpg","type":"image\/jpeg"}],"author":"admin","twitter_card":"summary_large_image","twitter_misc":{"Written by":"admin","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/fivemor.com\/?p=266763#article","isPartOf":{"@id":"https:\/\/fivemor.com\/?p=266763"},"author":{"name":"admin","@id":"https:\/\/fivemor.com\/#\/schema\/person\/b85e3c3dc0e1daea076524dc8810c371"},"headline":"A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions \u00bb Physics-Based Animation","datePublished":"2025-06-01T09:24:31+00:00","mainEntityOfPage":{"@id":"https:\/\/fivemor.com\/?p=266763"},"wordCount":161,"commentCount":0,"publisher":{"@id":"https:\/\/fivemor.com\/#organization"},"image":{"@id":"https:\/\/fivemor.com\/?p=266763#primaryimage"},"thumbnailUrl":"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/05\/blank.jpg","keywords":["Animation","Collisions","GaussSeidel","Generalized","PhysicallyCorrect","PhysicsBased","Robust","Simultaneous","Solver"],"articleSection":["Animation"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/fivemor.com\/?p=266763#respond"]}]},{"@type":"WebPage","@id":"https:\/\/fivemor.com\/?p=266763","url":"https:\/\/fivemor.com\/?p=266763","name":"A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions \u00bb Physics-Based Animation - Som2ny Network","isPartOf":{"@id":"https:\/\/fivemor.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/fivemor.com\/?p=266763#primaryimage"},"image":{"@id":"https:\/\/fivemor.com\/?p=266763#primaryimage"},"thumbnailUrl":"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/05\/blank.jpg","datePublished":"2025-06-01T09:24:31+00:00","breadcrumb":{"@id":"https:\/\/fivemor.com\/?p=266763#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/fivemor.com\/?p=266763"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/fivemor.com\/?p=266763#primaryimage","url":"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/05\/blank.jpg","contentUrl":"https:\/\/fivemor.com\/wp-content\/uploads\/2025\/05\/blank.jpg","width":200,"height":200},{"@type":"BreadcrumbList","@id":"https:\/\/fivemor.com\/?p=266763#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/fivemor.com\/?bp_activities=1"},{"@type":"ListItem","position":2,"name":"A Robust and Generalized Gauss-Seidel Solver for Physically-Correct Simultaneous Collisions \u00bb Physics-Based Animation"}]},{"@type":"WebSite","@id":"https:\/\/fivemor.com\/#website","url":"https:\/\/fivemor.com\/","name":"Som2ny Network","description":"Daily Deals","publisher":{"@id":"https:\/\/fivemor.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/fivemor.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/fivemor.com\/#organization","name":"Som2ny Network","url":"https:\/\/fivemor.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/fivemor.com\/#\/schema\/logo\/image\/","url":"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/07\/4a0953c4-logo-300x86-1.png","contentUrl":"https:\/\/fivemor.com\/wp-content\/uploads\/2026\/07\/4a0953c4-logo-300x86-1.png","width":300,"height":86,"caption":"Som2ny Network"},"image":{"@id":"https:\/\/fivemor.com\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/fivemor.com\/#\/schema\/person\/b85e3c3dc0e1daea076524dc8810c371","name":"admin","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/fivemor.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/729ae85bf62b9917e93538db2f2688ca?s=96&r=g&default=https%3A%2F%2Ffivemor.com%2Fwp-content%2Fplugins%2Fbuddypress-first-letter-avatar%2Fimages%2Fdefault%2F96%2Flatin_a.png","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/729ae85bf62b9917e93538db2f2688ca?s=96&r=g&default=https%3A%2F%2Ffivemor.com%2Fwp-content%2Fplugins%2Fbuddypress-first-letter-avatar%2Fimages%2Fdefault%2F96%2Flatin_a.png","caption":"admin"},"sameAs":["https:\/\/fivemor.com"],"url":"https:\/\/fivemor.com\/?author=1"}]}},"_links":{"self":[{"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/posts\/266763","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=266763"}],"version-history":[{"count":0,"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/posts\/266763\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=\/wp\/v2\/media\/245146"}],"wp:attachment":[{"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=266763"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=266763"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=266763"},{"taxonomy":"dealstore","embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fdealstore&post=266763"},{"taxonomy":"offerexpiration","embeddable":true,"href":"https:\/\/fivemor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fofferexpiration&post=266763"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}