{"id":876,"date":"2011-08-24T07:13:22","date_gmt":"2011-08-24T14:13:22","guid":{"rendered":"https:\/\/blogs.plm.automation.siemens.com\/t5\/Siemens-PLM-Corporate-Blog\/Conics-in-Geometric-Constraint-Solving\/ba-p\/334743"},"modified":"2026-03-26T11:03:06","modified_gmt":"2026-03-26T15:03:06","slug":"conics-in-geometric-constraint-solving","status":"publish","type":"post","link":"https:\/\/blogs.sw.siemens.com\/news\/conics-in-geometric-constraint-solving\/","title":{"rendered":"Conics in Geometric Constraint Solving"},"content":{"rendered":"<p><P>As their name implies, conic sections (or just \u201cconics\u201d) are curves that are created by intersecting a conical surface with a plane. They are usually&nbsp;divided into three types:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<BR \/><\/P><P style=\"text-align: center\"><BR \/><\/P><P style=\"text-align: center\"><A rel=\"attachment wp-att-6857 nofollow noopener noreferrer\" href=\"http:\/\/blog.industrysoftware.automation.siemens.com\/blog\/2011\/08\/24\/conics-geometric-constraint-solving\/conic_sections_www_text\/\"><IMG class=\"size-full wp-image-6857  aligncenter\" src=\"http:\/\/community.plm.automation.siemens.com\/legacyfs\/online\/wordpress\/images\/2011\/08\/conic_sections_www_text.jpg\" alt=\"\" width=\"399\" height=\"237\" \/><\/A>&nbsp;&nbsp;<\/P><BR \/>In the latest release of the <SPAN style=\"text-decoration: underline\"><A title=\"D-Cubed 2D DCM information\" href=\"http:\/\/www.plm.automation.siemens.com\/en_us\/products\/open\/d-cubed\/products\/2ddcm\/index.shtml\" rel=\"nofollow noopener noreferrer\">D-Cubed 2D DCM<\/A><\/SPAN>, we have introduced direct support for conics. As discussed in <SPAN style=\"text-decoration: underline\"><A title=\"geometric constraint solving and special cases\" href=\"http:\/\/blog.industrysoftware.automation.siemens.com\/blog\/2011\/08\/08\/geometric-constraint-solving-special-cases\/\" rel=\"nofollow noopener noreferrer\">my previous post<\/A><\/SPAN>, adding a new geometry type to the 2D DCM is a significant undertaking and I\u2019d like to talk about the benefits that this brings to users.&nbsp;&nbsp;&nbsp;&nbsp;<BR \/><BR \/><!--more-->One of the best explanations I have seen of why conics are used in CAD is from Adam O\u2019Hern on the <A title=\"CADjunkie\" href=\"http:\/\/cadjunkie.com\/\" rel=\"nofollow noopener noreferrer\">cadjunkie.com<\/A> site, in the <A title=\"conics in CAD\" href=\"http:\/\/cadjunkie.com\/1109\/tutorials_conics-101\/\" rel=\"nofollow noopener noreferrer\">Conics 101<\/A> tutorial. I definitely recommend viewing the video.&nbsp;<BR \/><BR \/>One of the points made by Adam is that conics can be defined in many different ways \u2013 for example: through 5 points, or tangent to 2 lines and through 3 points. This is where support for conics in a geometric constraint solver brings major benefits. In 2 dimensions, a conic has 5 degrees of freedom and the 2D DCM allows any consistent set of dimensions and constraints to be used to take up these freedoms and fully define the curve.&nbsp;<BR \/><BR \/>The following video shows examples of conics being manipulated in the 2D DCM demo application:&nbsp;<BR \/><BR \/><IFRAME width=\"425\" height=\"355\" src=\"https:\/\/www.youtube.com\/v\/_mwNItlxtC8\"><\/IFRAME>&nbsp;<BR \/><BR \/>With 2D DCM conics, engineers and designers have access to easy to use, powerful, constraint-driven methods which can create a wider range of models.&nbsp;<BR \/><BR \/>If you have any questions about conics get in touch and I\u2019ll do my best to help. Also, you can <SPAN style=\"text-decoration: underline\"><A title=\"request D-Cubed demo application\" href=\"http:\/\/www.plm.automation.siemens.com\/en_us\/products\/open\/d-cubed\/forms\/request-resources.cfm\" rel=\"nofollow noopener noreferrer\">request a copy of the D-Cubed demo application<\/A><\/SPAN> and try them yourself.&nbsp;&nbsp;&nbsp;<BR \/><BR \/>Mike<\/p>\n","protected":false},"excerpt":{"rendered":"<p>As their name implies, conic sections (or just \u201cconics\u201d) are curves that are created by intersecting a conical surface with a plane. They are usually&nbsp;divided into three types:&nbsp;&nbsp;&nbsp;&amp;&#8230;<\/p>\n","protected":false},"author":45687,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spanish_translation":"","french_translation":"","german_translation":"","italian_translation":"","polish_translation":"","japanese_translation":"","chinese_translation":"","footnotes":""},"categories":[1],"tags":[],"industry":[],"product":[],"coauthors":[],"class_list":["post-876","post","type-post","status-publish","format-standard","hentry","category-news"],"_links":{"self":[{"href":"https:\/\/blogs.sw.siemens.com\/news\/wp-json\/wp\/v2\/posts\/876","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.sw.siemens.com\/news\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.sw.siemens.com\/news\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.sw.siemens.com\/news\/wp-json\/wp\/v2\/users\/45687"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.sw.siemens.com\/news\/wp-json\/wp\/v2\/comments?post=876"}],"version-history":[{"count":1,"href":"https:\/\/blogs.sw.siemens.com\/news\/wp-json\/wp\/v2\/posts\/876\/revisions"}],"predecessor-version":[{"id":877,"href":"https:\/\/blogs.sw.siemens.com\/news\/wp-json\/wp\/v2\/posts\/876\/revisions\/877"}],"wp:attachment":[{"href":"https:\/\/blogs.sw.siemens.com\/news\/wp-json\/wp\/v2\/media?parent=876"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.sw.siemens.com\/news\/wp-json\/wp\/v2\/categories?post=876"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.sw.siemens.com\/news\/wp-json\/wp\/v2\/tags?post=876"},{"taxonomy":"industry","embeddable":true,"href":"https:\/\/blogs.sw.siemens.com\/news\/wp-json\/wp\/v2\/industry?post=876"},{"taxonomy":"product","embeddable":true,"href":"https:\/\/blogs.sw.siemens.com\/news\/wp-json\/wp\/v2\/product?post=876"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/blogs.sw.siemens.com\/news\/wp-json\/wp\/v2\/coauthors?post=876"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}