Computational Geometry

Piyush Kumar(Lecture 1: Introduction)

Welcome to CIS5930

Today

My Info : Timings for the classReferencesPre-RequisitesHow you will be gradedSyllabusAbout Computational Geometry and its applications

Befriend some simple concepts : Points, Vectors, Affine Spaces, Convexity ... ( Just old wine with new names )

Instructor

Piyush Kumar105B Love Building Ph: 850-645-2355Web page:

www.compgeom.com/~piyushEmail:

piyush@acm.org

Class Timings

To be announced in the first class. First Class at Love 0301 Wednesday, Jan 5th (5:15pm – 6:30pm)

Final Exam April 27th , Wednesday, 5:30 to 7:30pm.

References

Berg et.al CG and its applications (2nd ed)

Lecture notes from Dr. MountOther References Jirka Matousek’s

o Lectures on Discrete Geometry

My slides and notes Rourke’s ‘CG in C’

PreReq

Algorithms (COP 4530 or higher)C++ Basic Math skillsLot 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

o Both in theory (algorithm) and practice (code) Be better at applications that require geometric

algorithms:o Graphics, 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 : 25%Exam 1 : 25%Programming Assignments: 20%Final Project: 25%Project Presentation: 5%

* Modified from original announcement.

Theory

Real World

Syllabus*

NN SearchingConvexity and Convex hullsSegment intersection, Visibility and Polygon TriangulationLinear Programming and Quadratic Programming Perceptrons, SVMs and MEBs (ML)

Orthogonal Range Searching , Quad Trees and BSP Trees. Applications to Game Programming.

Point LocationVoronoi Diagram and Delaunay TriangulationsArrangements and applicationsRobot Motion PlanningDimension ReductionPopular Demand Topics - ?

Computational Geometry

What is it about ? Isnt the name self explanatory? Its tough to define an entire area

which lies in Math ∩ CS. There are always things on the edge, that become central with time.

We’ll move on and learn what we can…

What is it good for?

© Metris

© NASA

What kind of problems are you talking about?

Nearest Neighbor queries?

q

p

Collision detection

© Klosowski, Mitchell

Surface Reconstruction

Motion Planning

How does pioneer 10 move?© NASA

Find me a target?© Courtesy Kovan Research Lab

Machine Learning

Have I seen you before?

Geographic Information Systems

Courtesy USGS

Computational Fluid Dynamics

Model of pressure distribution over a CF-18 aircraft

Courtesy NRC/CNRC

The Beginning