Supporting Apparel Manufacturing


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  • Supporting Apparel Manufacturing

    1. 1. UMass Lowell Computer Science 91.504 Advanced Algorithms Computational Geometry Prof. Karen Daniels Spring, 2007 Lecture 1 Course Introduction
    2. 2. Course Introduction What is Computational Geometry?
    3. 3. Advanced Algorithms Computational Geometry Telecommunications Visualization 91.504 Computer Graphics Design Analyze Apply Core Geometric Algorithms Application-Based Algorithms CAD Manufacturing
    4. 4. Sample Application Areas Bioinformatics Medical Imaging Telecommunications Data Mining & Visualization Computer Graphics Geographic Information Systems Robotics Astrophysics
    5. 5. Typical Problems <ul><li>bin packing </li></ul><ul><li>Voronoi diagram </li></ul><ul><li>simplifying polygons </li></ul><ul><li>shape similarity </li></ul><ul><li>convex hull </li></ul><ul><li>maintaining line arrangements </li></ul><ul><li>polygon partitioning </li></ul><ul><li>nearest neighbor search </li></ul><ul><li>kd-trees </li></ul>SOURCE : Steve Skiena’s Algorithm Design Manual (for problem descriptions, see graphics gallery at )
    6. 6. Common Computational Geometry Structures source: O’Rourke, Computational Geometry in C Voronoi Diagram Convex Hull New Point Delaunay Triangulation
    7. 7. Sample Tools of the Trade <ul><li>Algorithm Design Patterns/Techniques: </li></ul><ul><ul><li>binary search divide-and-conquer duality </li></ul></ul><ul><ul><li>randomization sweep-line </li></ul></ul><ul><ul><li>derandomization parallelism </li></ul></ul><ul><li>Algorithm Analysis Techniques: </li></ul><ul><ul><li>asymptotic analysis, amortized analysis </li></ul></ul><ul><li>Data Structures: </li></ul><ul><ul><li>winged-edge, quad-edge, range tree, kd-tree </li></ul></ul><ul><li>Theoretical Computer Science principles: </li></ul><ul><ul><li>NP-completeness, hardness </li></ul></ul>Growth of Functions Summations Recurrences Sets Probability MATH Proofs Geometry Graph Theory Combinatorics Linear Algebra
    8. 8. Computational Geometry in Context Theoretical Computer Science Applied Computer Science Applied Math Geometry Computational Geometry Efficient Geometric Algorithms Design Analyze Apply
    9. 9. Course Introduction Course Description
    10. 10. Web Page
    11. 11. Nature of the Course <ul><li>Elective graduate Computer Science course </li></ul><ul><li>Theory and Practice </li></ul><ul><ul><li>Theory: “Pencil-and-paper” exercises </li></ul></ul><ul><ul><ul><li>design an algorithm </li></ul></ul></ul><ul><ul><ul><li>analyze its complexity </li></ul></ul></ul><ul><ul><ul><li>modify an existing algorithm </li></ul></ul></ul><ul><ul><ul><li>prove properties </li></ul></ul></ul><ul><ul><li>Practice </li></ul></ul><ul><ul><ul><li>Programs </li></ul></ul></ul><ul><ul><ul><li>Real-world examples </li></ul></ul></ul>
    12. 12. Course Structure: 2 Parts <ul><li>Basics </li></ul><ul><ul><li>Polygon Triangulation </li></ul></ul><ul><ul><li>Partitioning </li></ul></ul><ul><ul><li>Convex Hulls </li></ul></ul><ul><ul><li>Voronoi Diagrams </li></ul></ul><ul><ul><li>Arrangements </li></ul></ul><ul><ul><li>Search/Intersection </li></ul></ul><ul><ul><li>Motion Planning </li></ul></ul><ul><li>Advanced Topics </li></ul><ul><li>(sample topics) </li></ul><ul><li>(may change based on student interests) </li></ul><ul><ul><li>Covering </li></ul></ul><ul><ul><li>Clustering </li></ul></ul><ul><ul><li>Packing </li></ul></ul><ul><ul><li>Geometric Modeling </li></ul></ul><ul><ul><li>Topological Estimation </li></ul></ul>papers from literature Part 1 Part 2
    13. 13. Textbook <ul><li>Required: </li></ul><ul><ul><li>Computational Geometry in C </li></ul></ul><ul><ul><ul><li>second edition </li></ul></ul></ul><ul><ul><ul><li>by Joseph O’Rourke </li></ul></ul></ul><ul><ul><ul><li>Cambridge University Press </li></ul></ul></ul><ul><ul><ul><li>1998 </li></ul></ul></ul><ul><ul><ul><li>see course web site for ISBN number(s) & errata list </li></ul></ul></ul>can be ordered on-line Web Site: + conference, journal papers
    14. 14. Textbook Java Demo Applet <ul><li>Code function Chapter pointer directory </li></ul><ul><li>----------------------------------------------------- </li></ul><ul><li>Triangulate Chapter 1, Code 1.14 /tri </li></ul><ul><li>Convex Hull(2D) Chapter 3, Code 3.8 /graham </li></ul><ul><li>Convex Hull(3D) Chapter 4, Code 4.8 /chull </li></ul><ul><li>sphere.c Chapter 4, Fig. 4.15 /sphere </li></ul><ul><li>Delaunay Triang Chapter 5, Code 5.2 /dt </li></ul><ul><li>SegSegInt Chapter 7, Code 7.2 /segseg </li></ul><ul><li>Point-in-poly Chapter 7, Code 7.13 /inpoly </li></ul><ul><li>Point-in-hedron Chapter 7, Code 7.15 /inhedron </li></ul><ul><li>Int Conv Poly Chapter 7, Code 7.17 /convconv </li></ul><ul><li>Mink Convolve Chapter 8, Code 8.5 /mink </li></ul><ul><li>Arm Move Chapter 8, Code 8.7 /arm </li></ul>
    15. 15. Prerequisites <ul><li>Graduate Algorithms (91.503) </li></ul><ul><li>Coding experience in C, C++ </li></ul><ul><ul><li>Project coding may be done in Java if desired </li></ul></ul><ul><li>Standard CS graduate-level math prerequisites + high school Euclidean geometry </li></ul><ul><ul><li>additional helpful math background: </li></ul></ul><ul><ul><ul><li>linear algebra, topology </li></ul></ul></ul>Growth of Functions Summations Recurrences Sets Probability MATH Proofs Geometry
    16. 16. Syllabus (current plan) Part 1
    17. 17. Syllabus (current plan) Part 2
    18. 18. Important Dates <ul><li>Midterm Exam: Wednesday, 3/7 </li></ul><ul><ul><li>Open books, open notes </li></ul></ul><ul><li>Final Exam: none </li></ul>If you have conflicts with exam date, please notify me as soon as possible.
    19. 19. Grading <ul><li>Homework 35% </li></ul><ul><li>Project 35% </li></ul><ul><li>Midterm (O’Rourke) 30% (open book, notes ) </li></ul>* *Some project writeups may be eligible for submission to a computational geometry conference.
    20. 20. Machine Accounts <ul><li>Each student will have an account on my machine: </li></ul><ul><li>Username will be the same as your username on CS. </li></ul><ul><li>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. </li></ul><ul><li>To remotely log in, use a secure shell (e.g. ssh). </li></ul><ul><li>To transfer files, use a secure FTP (e.g. sftp). </li></ul><ul><li>LEDA and CGAL libraries are on minkowski. </li></ul>
    21. 21. Homework <ul><li>1 W 1/24 W 2/7 O’Rourke Chapter 1 </li></ul>HW# Assigned Due Content
    22. 22. Course Introduction My Computational Geometry Research
    23. 23. My Previous Applied Algorithms Research <ul><li>VLSI Design: </li></ul><ul><ul><li>Custom layout algorithms for silicon compiler </li></ul></ul><ul><li>Geometric Modeling: </li></ul><ul><ul><li>Partitioning cubic B-spline curves </li></ul></ul><ul><li>Manufacturing: </li></ul><ul><ul><li>see taxonomy on next slide </li></ul></ul>
    24. 24. Taxonomy of Problems Supporting Apparel Manufacturing Ordered Containment Geometric Restriction Distance-Based Subdivision Maximum Rectangle Limited Gaps Minimal Enclosure Column-Based Layout Two-Phase Layout Lattice Packing Core Algorithms Application-Based Algorithms Containment Maximal Cover
    25. 25. My Applied Algorithms Research Focus at UMass Lowell Telecommunications Data Mining, Visualization, Bioinformatics Manufacturing CAD Design Analyze Apply Application-Based Algorithms Core Geometric & Combinatorial Algorithms for covering, assignment, clustering, packing, layout feasibility, optimization problems