An un-summarized change.
This commit is contained in:
		
							
								
								
									
										30
									
								
								math/computational_geometry/notes.page
									
									
									
									
									
										Normal file
									
								
							
							
						
						
									
										30
									
								
								math/computational_geometry/notes.page
									
									
									
									
									
										Normal file
									
								
							@@ -0,0 +1,30 @@
 | 
				
			|||||||
 | 
					---
 | 
				
			||||||
 | 
					format: markdown
 | 
				
			||||||
 | 
					toc: yes
 | 
				
			||||||
 | 
					title: Computational Geometry Study Notes
 | 
				
			||||||
 | 
					...
 | 
				
			||||||
 | 
					
 | 
				
			||||||
 | 
					# Texts
 | 
				
			||||||
 | 
					
 | 
				
			||||||
 | 
					- *Discrete and Computational Geometry*
 | 
				
			||||||
 | 
					
 | 
				
			||||||
 | 
					# 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.
 | 
				
			||||||
 | 
					
 | 
				
			||||||
 | 
					
 | 
				
			||||||
 | 
					
 | 
				
			||||||
		Reference in New Issue
	
	Block a user