{"id":7805,"date":"2022-09-10T10:47:12","date_gmt":"2022-09-10T05:17:12","guid":{"rendered":"https:\/\/jassweb.com\/solved\/solved-check-whether-point-lies-strictly-inside-the-triangle\/"},"modified":"2022-09-10T10:47:12","modified_gmt":"2022-09-10T05:17:12","slug":"solved-check-whether-point-lies-strictly-inside-the-triangle","status":"publish","type":"post","link":"https:\/\/jassweb.com\/solved\/solved-check-whether-point-lies-strictly-inside-the-triangle\/","title":{"rendered":"[Solved] Check whether Point lies strictly inside the triangle"},"content":{"rendered":"<p> [ad_1]<br \/>\n<\/p>\n<div id=\"answer-48720340\" class=\"answer js-answer accepted-answer js-accepted-answer\" data-answerid=\"48720340\" data-parentid=\"48719711\" data-score=\"0\" data-position-on-page=\"1\" data-highest-scored=\"1\" data-question-has-accepted-highest-score=\"1\" itemprop=\"acceptedAnswer\" itemscope itemtype=\"https:\/\/schema.org\/Answer\">\n<div class=\"post-layout\">\n<div class=\"votecell post-layout--left\"><\/div>\n<div class=\"answercell post-layout--right\">\n<div class=\"s-prose js-post-body\" itemprop=\"text\">\n<p>There is  lot approaches to check whether point lies inside triangle. The simplest ones, I think: <\/p>\n<p>1) Check whether point is on the same side of all  edges (find signs of cross products for edge vectors and vertex-point vectors <code>AB x AP, BC x BP, CA x CP<\/code>)<\/p>\n<p>2) Represent AP vector in basis of AB and AC vectors &#8211; coefficients and their sum should be in range 0..1. Delphi code:<\/p>\n<pre><code>function PtInTriangle(ax, ay, bx, by, cx, cy, px, py: Integer): Boolean;\nvar\n  xb, yb, xc, yc, xp, yp, d: Integer;\n  bb, cc, oned: Double;\nbegin\n  Result := False;\n  xb := bx - ax;\n  yb := by - ay;\n  xc := cx - ax;\n  yc := cy - ay;\n  xp := px - ax;\n  yp := py - ay;\n  d := xb * yc - yb * xc;\n  if d &lt;&gt; 0 then begin\n    oned := 1 \/ d;\n    bb := (xp * yc - xc * yp) * oned;\n    cc := (xb * yp - xp * yb) * oned;\n    Result := (bb &gt; 0) and (cc &gt; 0) and (cc + bb &lt; 1);\n  end;\nend;\n<\/code><\/pre>\n<\/p><\/div>\n<div class=\"mt24\"><\/div>\n<\/div>\n<p>            <span class=\"d-none\" itemprop=\"commentCount\"><\/span> <\/p><\/div>\n<\/div>\n<p>[ad_2]<\/p>\n<p>solved Check whether Point lies strictly inside the triangle <\/p>\n","protected":false},"excerpt":{"rendered":"<p>[ad_1] There is lot approaches to check whether point lies inside triangle. The simplest ones, I think: 1) Check whether point is on the same side of all edges (find signs of cross products for edge vectors and vertex-point vectors AB x AP, BC x BP, CA x CP) 2) Represent AP vector in basis &#8230; <a title=\"[Solved] Check whether Point lies strictly inside the triangle\" class=\"read-more\" href=\"https:\/\/jassweb.com\/solved\/solved-check-whether-point-lies-strictly-inside-the-triangle\/\" aria-label=\"More on [Solved] Check whether Point lies strictly inside the triangle\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[320],"tags":[2186,739],"class_list":["post-7805","post","type-post","status-publish","format-standard","hentry","category-solved","tag-computational-geometry","tag-geometry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>[Solved] Check whether Point lies strictly inside the triangle - JassWeb<\/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:\/\/jassweb.com\/solved\/solved-check-whether-point-lies-strictly-inside-the-triangle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Solved] Check whether Point lies strictly inside the triangle - JassWeb\" \/>\n<meta property=\"og:description\" content=\"[ad_1] There is lot approaches to check whether point lies inside triangle. 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