From 84af95d8180ebbc0350372eaacc242d5b1642235 Mon Sep 17 00:00:00 2001 From: Levi Pearson Date: Sat, 25 Jan 2014 00:10:01 -0700 Subject: [PATCH] Some more notes --- math/computational_geometry/notes.page | 13 +++++++++++++ 1 file changed, 13 insertions(+) diff --git a/math/computational_geometry/notes.page b/math/computational_geometry/notes.page index c2a1451..88ec5dc 100644 --- a/math/computational_geometry/notes.page +++ b/math/computational_geometry/notes.page @@ -32,3 +32,16 @@ parallel to an edge passes through an odd number of edges. A point $x$ is *exterior* if a ray through it ... etc ... passes through an even number of edges. + +These two facts form the basis of an algorithm for determining whether +a point is inside a polygon. + +*diagonal* +: A line segment of $P$ connecting two vertices and lying in the interior of +$P$, not touching $\partial P$ except at endpoints. Two diagonals are +*noncrossing* if they share no interior points. + +*triangulation* +: A decomposition of $P$ into triangles by a maximal set of +noncrossing diagonals. Maximal means that no more diagonals may be +added without crossing.