Changes

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