From b6fbf235ee11a2aec6597c152446af17f37278d2 Mon Sep 17 00:00:00 2001 From: Levi Pearson Date: Fri, 24 Jan 2014 23:23:09 -0700 Subject: [PATCH] Re-make changes --- math/computational_geometry/notes.page | 20 ++++++++++++-------- 1 file changed, 12 insertions(+), 8 deletions(-) diff --git a/math/computational_geometry/notes.page b/math/computational_geometry/notes.page index 284d925..881a0ce 100644 --- a/math/computational_geometry/notes.page +++ b/math/computational_geometry/notes.page @@ -6,7 +6,7 @@ title: Computational Geometry Study Notes # Texts -- *Discrete and Computational Geometry* +- *Discrete and Computational Geometry*, Devadoss # Reading Notes @@ -17,14 +17,18 @@ Computational Geometry is *discrete* rather than *continuous* Fundamental building blocks are the *point* and line *segment*. *polygon* -: the closed region of the plane bounded by a finite collection of line segments -forming a closed curve that does not intersect itself. The segments are called *edges* -and the points where they meet are *vertices*. The set of vertices and edges is the *boundary*. +: the closed region of the plane bounded by a finite collection of +line segments forming a closed curve that does not intersect +itself. The segments are called *edges* and the points where they meet +are *vertices*. The set of vertices and edges is the *boundary*. **Theorem 1.1: Polygonal Jordan Curve** -:The boundary $\partial P$ of a polygon $P$ partitions the plane into two parts. -In particular, the two components of $\Bbb{R}^2\setminus \partial P$ are the -bounded interior and the unbounded exterior. - +:The boundary $\partial P$ of a polygon $P$ partitions the plane into +two parts. In particular, the two components of $\Bbb{R}^2\setminus +\partial P$ are the bounded interior and the unbounded exterior. +A point $x$ is *interior* if a ray through it in a fixed direction not +parallel to an edge passes through an odd number of edges. +A point $x$ is *exterior$ if a ray through it ... etc ... through an +even number of edges.