UMass Lowell Computer Science Advanced Algorithms Computational Geometry Prof. Karen Daniels Spring, 2007 Lecture 1 Course Introduction

What is Computational Geometry?

Advanced Algorithms Computational Geometry Telecommunications Visualization Manufacturing ComputerGraphics Design Analyze Apply CAD

Sample Application Areas Computer Graphics Geographic Information Systems Robotics Bioinformatics Astrophysics MedicalImaging Telecommunications Data Mining & Visualization

Typical Problems ä bin packing ä Voronoi diagram ä simplifying polygons ä shape similarity ä convex hull ä maintaining line arrangements ä polygon partitioning ä nearest neighbor search ä kd-trees SOURCE: Steve Skiena’s Algorithm Design Manual (for problem descriptions, see graphics gallery at ) (for problem descriptions, see graphics gallery at

Common Computational Geometry Structures Voronoi Diagram Convex Hull New Point source: O’Rourke, Computational Geometry in C Delaunay Triangulation

Sample Tools of the Trade Algorithm Design Patterns/Techniques: binary searchdivide-and-conquerduality randomizationsweep-line derandomizationparallelism Algorithm Analysis Techniques: asymptotic analysis, amortized analysis Data Structures: winged-edge, quad-edge, range tree, kd-tree Theoretical Computer Science principles: NP-completeness, hardness Growth of Functions Summations Recurrences Sets Probability MATH Proofs Geometry Graph Theory Combinatorics Linear Algebra

Computational Geometry in Context TheoreticalComputerScience Applied Computer Science AppliedMath Geometry ComputationalGeometryEfficient Geometric Algorithms Design Analyze Apply

Course Introduction Course Description

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Nature of the Course ä Elective graduate Computer Science course ä Theory and Practice ä Theory: “Pencil-and-paper” exercises ä design an algorithm ä analyze its complexity ä modify an existing algorithm ä prove properties ä Practice ä Programs ä Real-world examples

Course Structure: 2 Parts Basics Polygon Triangulation Partitioning Convex Hulls Voronoi Diagrams ArrangementsSearch/Intersection Motion Planning Advanced Topics (sample topics) (sample topics) (may change based on student interests) CoveringClusteringPacking Geometric Modeling Topological Estimation papers from literature

Textbook - - Required: ä Computational Geometry in C ä second edition ä by Joseph O’Rourke ä Cambridge University Press ä 1998 ä see course web site for ISBN number(s) & errata list can be ordered on-line Web Site: + conference, journal papers

Textbook Java Demo Applet Code functionChapter pointerdirectory TriangulateChapter 1, Code 1.14/tri Convex Hull(2D)Chapter 3, Code 3.8/graham Convex Hull(3D)Chapter 4, Code 4.8/chull sphere.cChapter 4, Fig. 4.15/sphere Delaunay Triang Chapter 5, Code 5.2/dt SegSegIntChapter 7, Code 7.2/segseg Point-in-polyChapter 7, Code 7.13/inpoly Point-in-hedronChapter 7, Code 7.15/inhedron Int Conv PolyChapter 7, Code 7.17/convconv Mink ConvolveChapter 8, Code 8.5/mink Arm Move Chapter 8, Code 8.7/arm

Prerequisites ä Graduate Algorithms (91.503) ä Coding experience in C, C++ ä Project coding may be done in Java if desired ä Standard CS graduate-level math prerequisites + high school Euclidean geometry ä additional helpful math background: ä linear algebra, topology Growth of Functions Summations Recurrences Sets Probability MATH Proofs Geometry

Syllabus (current plan)

Important Dates ä Midterm Exam:Wednesday, 3/7 ä Open books, open notes ä Final Exam:none If you have conflicts with exam date, please notify me as soon as possible.

Grading ä ä Homework35% ä ä Project35% ä ä Midterm (O’Rourke) 30% (open book, notes ) * *Some project writeups may be eligible for submission to a computational geometry conference.

Machine Accounts ä Each student will have an account on my machine: minkowski.cs.uml.edu. ä Username will be the same as your username on CS. ä Password will be your initials followed by the last 5 digits on the bottom right hand corner of the back of your student id card. ä To remotely log in, use a secure shell (e.g. ssh). ä To transfer files, use a secure FTP (e.g. sftp). ä LEDA and CGAL libraries are on minkowski.

Homework 1 W 1/24 W 2/7 O’Rourke Chapter 1 HW# Assigned Due Content

Course Introduction My Computational Geometry Research

My Previous Applied Algorithms Research ä VLSI Design: ä Custom layout algorithms for silicon compiler ä Geometric Modeling: ä Partitioning cubic B- spline curves ä Manufacturing: ä see taxonomy on next slide

Taxonomy of Problems Supporting Apparel Manufacturing OrderedContainment Geometric Restriction Distance-BasedSubdivision MaximumRectangle Limited Gaps MinimalEnclosure Column-Based Layout Two-Phase Layout LatticePacking Containment Maximal Cover

My Applied Algorithms Research Focus at UMass Lowell Telecommunications Data Mining, Visualization,Bioinformatics Manufacturing Design Analyze Apply for covering, assignment, clustering, packing, layout feasibility, optimization problems CAD