wiki/math/computational_geometry/notes.page

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title: Computational Geometry Study Notes
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# Texts

- *Discrete and Computational Geometry*, Devadoss

# Reading Notes

## *Devadoss*, 24 Jan 2014

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*.

**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.

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 ... passes
through an even number of edges.