{"id":320,"date":"2011-06-27T21:03:46","date_gmt":"2011-06-27T21:03:46","guid":{"rendered":"http:\/\/devnot.wordpress.com\/?p=320"},"modified":"2019-12-15T15:23:09","modified_gmt":"2019-12-15T14:23:09","slug":"find-out-where-a-vector-intersects-a-horizontal-or-vertical-line","status":"publish","type":"post","link":"https:\/\/thomas-jansen.eu\/?p=320","title":{"rendered":"Find out where a vector intersects a horizontal (or vertical) line"},"content":{"rendered":"\n\n\n

Of course the line intersection method can be used but in case of horizontal or vertical lines a quicker solution is available.<\/p>\n\n\n\n

Assume  the vector V1 defined by points P1 and P2. and the horizontal line is  through point P<\/p>\n\n\n\n

The offset of the intersection is:<\/p>\n\n\n\n

\"offset = \dfrac{P_y - P1_y}{P2_y - P1_y}\"<\/pre>\n\n\n\n
Lets say P1 is 10,10 P2 20,20 and P.y 0,15<\/p>\n\n\n\n
In this case  (15-10)\/(20-10)  is 0.5<\/p>\n\n\n\n
If P1 and P2 is revered it will be (15-20)\/(10-20) = -5\/-10 = 0.5.<\/p>\n\n\n\n
Note:<\/strong>
There is a\u00a0 special case if the vector is parallel or on the horizontal line, in that case, there is no intersection. In that case, p2.y\u00a0– p1y is zero. This situation must be checked since it will also prevent a division by zero. You probably also want to limit very small values of this value since it may result in very large (positive or negatively) offset values.<\/p>\n\n\n\n
Vertical lines:<\/strong>
In case of a vertical line replace all .y above by x.<\/p>\n\n\n\n
Calculating the intersection point:<\/strong>
The offset when the vector is hit is always >= 0.0 and <= 1.0,\u00a0 otherwise, it is on the extended vector.<\/p>\n\n\n\n
Calculating the intersection point on the(extended)  vector is trivial<\/p>\n\n\n\n
\"x = p1_x +(p2_x-p1_x) * offset\"\n\"y = p1_y +(p2_y-p1_y) * offset\"<\/pre>\n\n\n\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
Of course the line intersection method can be used but in case of horizontal or vertical lines a quicker solution is available. Assume  the vector V1 defined by points P1 and P2. and the horizontal line is  through point P The offset of the intersection is: $offset = \\dfrac{P_y – P1_y}{P2_y – P1_y}$ Lets say […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-320","post","type-post","status-publish","format-standard","hentry","category-geometry"],"_links":{"self":[{"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/posts\/320","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=320"}],"version-history":[{"count":2,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/posts\/320\/revisions"}],"predecessor-version":[{"id":617,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=\/wp\/v2\/posts\/320\/revisions\/617"}],"wp:attachment":[{"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=320"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=320"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thomas-jansen.eu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=320"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}