Computational Geometry Piyush Kumar (Lecture 1: Introduction) Welcome to CIS5930

Today My Info : Timings for the class References Pre-Requisites How you will be graded Syllabus About Computational Geometry  and its applications Befriend some simple concepts :  Points, Vectors, Affine Spaces, Convexity...  ( Just old wine with new names )

Instructor Piyush Kumar 161 Love Building Ph: Web page: piyush at acm.Dot. org

Class Timings To be announced in the first class.  First Class at Love 0103  Monday, Jan 7 th (2:30pm – 3:20pm) Final Exam  May 3rd

References Berg et.al  CG and its applications (2 nd ed) Lecture notes from Dr. Mount Other References  Jirka Matousek’s oLectures on Discrete Geometry  My slides and notes  Rourke’s ‘CG in C’

PreReq Algorithms (COP 4530 or higher) C++ Basic Math skills Lot of Time to hack the course.

What can you expect? After the course expect to  Know more about geometric algorithms (of course)  Think geometrically  Know how to solve geometric problems oBoth in theory (algorithm) and practice (code)  Be better at applications that require geometric algorithms: oGraphics, Visualization, Game programming, Robotics, … o(and applications you never imagined could use geometry)  Expect to meet some big shots in CG during the course or just afterwards.

Grading* Homework : 15% Exams : 45% Programming Assignments: 15% Final Project: 15% Project Presentation: 10% * Modified from original announcement. Theory Real World

Computational Geometry Design and analysis of algorithms involving geometric IO. Has been an active area since late 70s. Deals with discrete nature of geometric problems, as opposed to continuous issues.

Computational Geometry Its tough to define an entire area which lies in Math ∩ CS ∩ Application Areas. There are always things on the edge, that become central with time. We’ll move on and learn what we can…

Computational Geometry Strengths  Development of Geometric Tools  Provable Efficiency  Correctness/Robustness  Linkage to discrete combinatorial geometry.

Computational Geometry Weaknesses  Continuous problems.  Emphasis on flat objects.  Emphasis on Low-dimensional problems.

Syllabus* NN Searching Convexity and Convex hulls Segment intersection, Visibility and Polygon Triangulation Linear Programming and Quadratic Programming  Perceptrons, SVMs and MEBs (ML) Orthogonal Range Searching, Quad Trees and BSP Trees.  Applications to Game Programming. Point Location Voronoi Diagram and Delaunay Triangulations Arrangements and applications Robot Motion Planning Dimension Reduction Popular Demand Topics - ?

What is it good for?

© Metris © NASA

What kind of problems are you talking about? Nearest Neighbor queries? q p

Collision detection © Klosowski, Mitchell, Govindaraju et.al.

Surface Reconstruction

Motion Planning How does pioneer 10 move? © NASA Find me a target? © Courtesy Kovan Research Lab

Machine Learning A plane in a non-linear lifting.

Geographic Information Systems Courtesy USGS

Computational Fluid Dynamics Model of pressure distribution over a CF-18 aircraft Courtesy NRC/CNRC

The Beginning