From c488aac4c054578bcf791022afc1590100cbe708 Mon Sep 17 00:00:00 2001 From: Levi Pearson Date: Fri, 24 Jan 2014 23:00:18 -0700 Subject: [PATCH] Changes --- math/computational_geometry/notes.page | 20 ++++++++------------ 1 file changed, 8 insertions(+), 12 deletions(-) diff --git a/math/computational_geometry/notes.page b/math/computational_geometry/notes.page index 881a0ce..284d925 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*, Devadoss +- *Discrete and Computational Geometry* # Reading Notes @@ -17,18 +17,14 @@ 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.