UMass Lowell Computer Science 91 504 Advanced Algorithms

UMass Lowell Computer Science 91. 504 Advanced Algorithms Computational Geometry Prof. Karen Daniels Spring, 2010 Lecture 1 Course Introduction

Course Introduction What is Computational Geometry?

Advanced Algorithms Computational Geometry Computer Graphics Visualization Design Analyze Covering for Geometric Modeling feasibility, estimation, optimization problems for covering, assignment, clustering, packing, layout, geometric modeling Data Mining, Clustering, for Bioinformatics Apply Packing for Manufacturing Meshing for Geometric Modeling Courtesy of Cadence Design Systems Topological Invariant Estimation for Geometric Modeling CAD

Typical Problems • bin packing • • Voronoi diagram simplifying polygons • shape similarity • convex hull • maintaining line arrangements • • polygon partitioning nearest neighbor search • kd-trees SOURCE: Steve Skiena’s Algorithm Design Manual (for problem descriptions, see graphics gallery at http: //www. cs. sunysb. edu/~algorith)

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

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

Computational Geometry in Context Geometry Design Applied Math Analyze Computational Geometry Efficient Geometric Algorithms Apply Applied Computer Science Theoretical Computer Science

Course Introduction Course Description

Web Page http: //www. cs. uml. edu/~kdaniels/courses/ALG_504_S 10. html

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

Course Structure: 2 Parts Basics Polygon Triangulation Partitioning Convex Hulls Voronoi Diagrams Arrangements Search/Intersection Motion Planning Advanced Topics (sample topics) (may change based on student interests) Covering Clustering Packing Courtesy of Cadence Design Systems Geometric Modeling Topological Estimation papers from literature

Textbooks • Required: • Computational Geometry in C • second edition by Joseph O’Rourke Cambridge University Press 1998 • see course web site for ISBN number(s) & errata list • • • Ordered for UML bookstore and can be ordered on-line Web Site: http: //cs. smith. edu/~orourke/books/compgeom. html + conference, journal papers

Textbook Java Demo Applet Code function Chapter pointer directory --------------------------Triangulate Chapter 1, Code 1. 14 /tri Convex Hull(2 D) Convex Hull(3 D) sphere. c Delaunay Triang Seg. Int Point-in-poly Point-in-hedron Int Conv Poly Mink Convolve Arm Move Chapter Chapter Chapter 3, 4, 4, 5, 7, 7, 8, 8, Code 3. 8 Code 4. 8 Fig. 4. 15 Code 5. 2 Code 7. 13 Code 7. 15 Code 7. 17 Code 8. 5 Code 8. 7 /graham /chull /sphere /dt /segseg /inpoly /inhedron /conv /mink /arm http: //cs. smith. edu/~orourke/books/Comp. Geom. html

Textbooks • Required: • Computational Geometry: Algorithms & Applications • third edition by de Berg, Cheong, van Kreveld, Overmars Springer 2008 • see course web site for ISBN number • • • Ordered for UML bookstore and can be ordered on-line Web Site: http: //www. cs. uu. nl/geobook + conference, journal papers

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: linear algebra, topology MATH Summations Sets ä Growth of Functions Probability Proofs Geometry Recurrences

Syllabus (current plan)

Syllabus (current plan)

Important Dates • Midterm Exam: • • Thursday, 3/11 Open books, open notes Final Exam: none If you have conflicts with exam date, please notify me as soon as possible.

Grading • • • Homework Project * Midterm (O’Rourke) 35% 30% (open book, notes ) *Some project writeups may be eligible for submission to a computational geometry conference.

Homework HW# Assigned 1 Th 1/28 Due Th 2/11 Content O’Rourke Chapters 1, 2 de Berg Chapters 1, 3 CGAL documentation

Course Introduction My Geometry Related Research

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

Taxonomy of Problems Supporting Apparel Manufacturing Maximum Rectangle Geometric Restriction Distance-Based Subdivision Ordered Containment Limited Gaps Containment Maximal Cover Two-Phase Layout Minimal Enclosure Lattice Packing Column-Based Layout

to be continued in another slide show