Re-make changes

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
+: the closed region of the plane bounded by a finite collection of
-forming a closed curve that does not intersect itself. The segments are called *edges*
+line segments forming a closed curve that does not intersect
-and the points where they meet are *vertices*. The set of vertices and edges is the *boundary*.
+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.
+:The boundary $\partial P$ of a polygon $P$ partitions the plane into
-In particular, the two components of $\Bbb{R}^2\setminus \partial P$ are the
+two parts.  In particular, the two components of $\Bbb{R}^2\setminus
-bounded interior and the unbounded exterior.
+\partial P$ 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.