CormenCG - UMass Lowell Computer Science Prof. Karen...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
UMass Lowell Computer Science Prof. Karen Daniels Computational Geometry Overview from Cormen, et al. Chapter 33
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Overview Line Segment Intersection Convex Hull Algorithms Nearest Neighbors/Closest Points
Background image of page 2
Line Segment Intersections (2D) Intersection of 2 Line Segments Intersection of > 2Line Segments
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Cross-Product-Based Geometric Primitives source: 91.503 textbook Cormen et al. p 0 p 2 p 1 (1) p 1 p 3 p 2 (2) p 2 p 1 p 3 p 4 (3) Some fundamental geometric questions:
Background image of page 4
Cross-Product-Based Geometric Primitives: (1) source: 91.503 textbook Cormen et al. Advantage : less sensitive to accumulated round-off error 1 2 2 1 2 1 2 1 2 1 det y x y x y y x x p p p 0 p 2 p 1 (1) 33.1
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Cross-Product-Based Geometric Primitives: (2) source: 91.503 textbook Cormen et al. p 0 p 2 p 1 (2) 33.2
Background image of page 6
Intersection of 2 Line Segments source: 91.503 textbook Cormen et al. p 2 p 1 p 3 p 4 (3) Step 1 : Bounding Box Test Step 2 : Does each segment straddle the line containing the other? 33.3 p3 and p4 on opposite sides of p1p2
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Segment-Segment Intersection Finding the actual intersection point Approach: parametric vs. slope/intercept parametric generalizes to more complex intersections e.g. segment/triangle Parameterize each segment Intersection: values of s , t such that p(s) = q(t) : a+sA = c+tC a b c d L ab L cd a b c d L ab L cd A=b-a p(s)=a+sA q(t)=c+tC C=d-c source: O’Rourke, Computational Geometry in C 2 equations in unknowns s , t : 1 for x, 1 for y
Background image of page 8
Demo Segment/Segment Intersection http://cs.smith.edu/~orourke/books/CompGeom/CompGeom.html
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Intersection of >2 Line Segments source: 91.503 textbook Cormen et al. Sweep-Line Algorithmic Paradigm: 33.4
Background image of page 10
Intersection of >2 Line Segments source: 91.503 textbook Cormen et al. Sweep-Line Algorithmic Paradigm:
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
source: 91.503 textbook Cormen et al. Time to detect if any 2 segments intersect: O(n lg n) source: 91.503 textbook Cormen et al. 33.5 Note that it exits as soon as one intersection is detected. Balanced BST stores segments in order
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/13/2012 for the course CS 91.504 taught by Professor Daniels during the Spring '10 term at UMass Lowell.

Page1 / 37

CormenCG - UMass Lowell Computer Science Prof. Karen...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online