Computational Geometry
Aritra Banik
School of Computer Sciences
National Institute of Science Education and Research, HBNI
CS 456, CS 662 Computational Geometry
Class Meetings Tuesday 10:30-12 Friday 13:30-15:00
Tutorial Wednesday 13:30-15:00, Thursday 8:30-9:25
The necessary evil - marks, exam, etc. midterm + final + assignments. Grading will be relative
Webpage http://www.niser.ac.in/ aritra/CG All the slides will be on the webpage
Assignment 1 is in the webpage,Deadline 12.01.2020
CS 456, CS 662 Computational Geometry
Class Meetings Tuesday 10:30-12 Friday 13:30-15:00
Tutorial Wednesday 13:30-15:00, Thursday 8:30-9:25 The necessary evil - marks, exam, etc.
midterm + final + assignments.
Grading will be relative
Webpage http://www.niser.ac.in/ aritra/CG All the slides will be on the webpage
Assignment 1 is in the webpage,Deadline 12.01.2020
CS 456, CS 662 Computational Geometry
Class Meetings Tuesday 10:30-12 Friday 13:30-15:00
Tutorial Wednesday 13:30-15:00, Thursday 8:30-9:25 The necessary evil - marks, exam, etc.
midterm + final + assignments.
Grading will be relative
Webpage http://www.niser.ac.in/ aritra/CG All the slides will be on the webpage
Assignment 1 is in the webpage,Deadline 12.01.2020
CS 456, CS 662 Computational Geometry
Class Meetings Tuesday 10:30-12 Friday 13:30-15:00
Tutorial Wednesday 13:30-15:00, Thursday 8:30-9:25 The necessary evil - marks, exam, etc.
midterm + final + assignments.
Grading will be relative
Webpage http://www.niser.ac.in/ aritra/CG All the slides will be on the webpage
Assignment 1 is in the webpage,Deadline 12.01.2020
Computational Geometry
Study of algorithms for geometric problems
CG
Computer Graphics
Computer Vision
VLSI
Robotics (motion planning) Computer
aided design Molecular
Biology
CG is a sub-discipline of algorithms and complexity. Significant interaction withdiscrete mathematics.
Computational Geometry
Study of algorithms for geometric problems
CG
Computer Graphics
Computer Vision
VLSI
Robotics (motion planning) Computer
aided design Molecular
Biology
CG is a sub-discipline of algorithms and complexity.
Significant interaction withdiscrete mathematics.
Example Problems
Range Searching
Location Queries
Closest pair of points: Given a set of points, find the two with the smallest distance from each other
Triangulation: Mesh generation
Example Problems
Range Searching Location Queries
Closest pair of points: Given a set of points, find the two with the smallest distance from each other
Triangulation: Mesh generation
Example Problems
Range Searching Location Queries
Closest pair of points: Given a set of points, find the two
Triangulation: Mesh generation
Example Problems
Range Searching Location Queries
Closest pair of points: Given a set of points, find the two with the smallest distance from each other
Triangulation: Mesh generation
Taste of Comb. Geometry
Helly’s Theorem: Let C1· · ·Cnbe a family of convex sets in the plane. If every triple intersects, then ∩Ci is non-empty.
Center Points: Given points p1· · ·pn in the plane, a point x is called center point if any line through x contains at least n/3 points on each side.
Ham Sandwich Theorem: Take nred points and nblue points in the plane. There is a line simultaneously bisecting both red and blue points.
Elementary Objects
Point p= (x, y), wherex, y reals.
Line `:y=mx+c Line segment s= [p, q].
Circle C= (p, r). (Center, radius) Polygon < p1, p2, ..., pn>.
p1
p2
pn
Elementary Operations
Is point pon line `?
Is point pinside or outside circle C?
Do segments s1 and s2 intersect?
Is point pinside or outside polygon P?
Overview of the Course
Convex Hull
Line Sweep Method Triangulation of Arbitrary Polygon.
Visibility Problems Planar Point Location Voronoi Diagram and Delaunay Triangulation.
Randomized Incremental Construction
Intersection of Half Planes and Duality
Line arrangements, Levels Range Searching
Quadtrees
Well separated pair decomposition
Geometric Graph Classes Interval Graphs, UDG Geometric Set Cover Approximation
Algorithms for Geometric Intersection Graphs 1 Local Search