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Levi Pearson 2014-01-24 23:00:18 -07:00
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@ -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.