CG_Lecture1a - UMass Lowell Computer Science 91.504...

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Unformatted text preview: UMass Lowell Computer Science 91.504 Advanced Algorithms Computational Geometry Prof. Karen Daniels Spring, 2010 Spring Lecture 1 Course I t d ti C 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 Meshing for Geometric Modeling Packing for Manufacturing Courtesy of Cadence Design Systems Topological Invariant Estimation for Geometric Modeling g CAD Typical Problems bin packing Voronoi diagram simplifying polygons shape similarity convex hull maintaining line g arrangements polygon partitioning nearest neighbor search kdkd-trees SOURCE: SOURCE: Steve Skiena's Algorithm Design Manual (for problem descriptions, see graphics gallery at ) 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 D i P tt Al ith Design Patterns/Techniques: /T h i binary search divide-and-conquer divide-andrandomization sweep-line sweepderandomization parallelism duality Algorithm Analysis Techniques: asymptotic analysis, amortized analysis Data Structures: wingedwinged-edge, quad-edge, range tree, kd-tree quadkd- Theoretical Computer Science principles: Th i lC S i i i l NPNP-completeness, hardness MATH Sets Summations Probability Growth of Functions Combinatorics Proofs Geometry Linear Algebra Recurrences Graph Theory Computational Geometry in Context Geometry Design D i Applied pp Math Analyze A l Theoretical Computer Science Computational Geometry Efficient Geometric Algorithms Apply Applied Computer Science Course Introduction Course Description Web Page Nature of the Course Elective graduate Computer Science course Theory and Practice Theory: "Pencil-and-paper" exercises "Pencil-and design an algorithm analyze its complexity modify an existing algorithm prove properties Programs RealReal-world examples Practice Course Structure: 2 Parts Basics Polygon Triangulation Partitioning P ii i Convex Hulls Voronoi Diagrams Arrangements Search/Intersection Motion Planning Covering Clustering Packing Courtesy of Cadence Design Systems Advanced Topics (sample topics) (may change based on student interests) Geometric Modeling Topological Estimation papers from literature Textbooks Required: q 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: + conference, journal papers Textbook Java Demo Applet Code function Chapter pointer directory ----------------------------------------------------Triangulate Chapter 1, Code 1.14 /tri Convex Hull(2D) Convex Hull(3D) sphere.c Delaunay Triang SegSegInt Point-inPoint-in-poly Point-inPoint-in-hedron Int Conv Poly Mink Convolve Arm Move Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter 3, 4, 4, 5, 7, 7, 7, 7, 8, 8, Code 3.8 Code 4.8 Fig. 4.15 Code 5.2 Code 7.2 Code 7.13 Code 7.15 Code 7.17 Code 8.5 Code 8.7 /graham /chull /sphere /dt /segseg /inpoly /inhedron /convconv /mink /arm / Textbooks Required: q Computational Geometry: Algorithms & Applications third edition by de Berg, Cheong, van Kreveld, Kreveld, Overmars Overmars Springer 2008 see course web site for ISBN number Ordered for UML bookstore and can be ordered on-line Web Site: + conference, journal papers Prerequisites Graduate Algorithms (91.503) (91 503) Coding experience in C, C++ Project di P j t coding may be done in Java if desired b d i J d i d Standard CS graduate-level math graduateprerequisites + high school E lid i it hi h h l Euclidean geometry additional helpful math background: linear algebra, topology MATH Summations S mmations Sets Growth of Functions Probability Proofs Geometry Recurrences Syllabus (current plan) Syllabus (current plan) Important Dates Midterm Exam: Thursday, 3/11 none Open b k open notes O books, Final Exam: If you have conflicts with exam date, please notify me as soon as possible. Grading Homework Project * Midterm (O'Rourke) 35% 35% 30% (open book, notes ) *Some project writeups may be eligible for submission Some to a computational geometry conference. Homework HW# Assigned 1 Th 1/28 Due Th 2/11 Content O'Rourke Chapters 1,2 p , de Berg Chapters 1, 3 CGAL documentation Course Introduction My Geometry Related Research My Previous Applied Algorithms Research VLSI Design: Custom layout algorithms for silicon compiler Partitioning cubic BBp spline curves see taxonomy on next y slide Geometric Modeling: Manufacturing: Taxonomy of Problems Supporting Apparel Manufacturing Maximum a u Rectangle Geometric Restriction DistanceDistance-Based Subdivision Limited Gaps Containment Minimal Enclosure Ordered Containment Maximal Cover TwoTwo-Phase Layout Lattice Packing ColumnColumn-Based Layout to be continued in another slide show ...
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