# Supporting Apparel Manufacturing

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## Supporting Apparel ManufacturingPresentation Transcript

• UMass Lowell Computer Science 91.504 Advanced Algorithms Computational Geometry Prof. Karen Daniels Spring, 2007 Lecture 1 Course Introduction
• Course Introduction What is Computational Geometry?
• Advanced Algorithms Computational Geometry Telecommunications Visualization 91.504 Computer Graphics Design Analyze Apply Core Geometric Algorithms Application-Based Algorithms CAD Manufacturing
• Sample Application Areas Bioinformatics Medical Imaging Telecommunications Data Mining & Visualization Computer Graphics Geographic Information Systems Robotics Astrophysics
• 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 source: O’Rourke, Computational Geometry in C Voronoi Diagram Convex Hull New Point Delaunay Triangulation
• Sample Tools of the Trade
• Algorithm Design Patterns/Techniques:
• binary search divide-and-conquer duality
• randomization sweep-line
• derandomization parallelism
• 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 Theoretical Computer Science Applied Computer Science Applied Math Geometry Computational Geometry Efficient Geometric Algorithms Design Analyze Apply
• Course Introduction Course Description
• Web Page http://www.cs.uml.edu/~kdaniels/courses/ALG_504.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
• (sample topics)
• (may change based on student interests)
• Covering
• Clustering
• Packing
• Geometric Modeling
• Topological Estimation
papers from literature Part 1 Part 2
• Textbook
• 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
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(2D) Chapter 3, Code 3.8 /graham
• Convex Hull(3D) Chapter 4, Code 4.8 /chull
• sphere.c Chapter 4, Fig. 4.15 /sphere
• Delaunay Triang Chapter 5, Code 5.2 /dt
• SegSegInt Chapter 7, Code 7.2 /segseg
• Point-in-poly Chapter 7, Code 7.13 /inpoly
• Point-in-hedron Chapter 7, Code 7.15 /inhedron
• Int Conv Poly Chapter 7, Code 7.17 /convconv
• Mink Convolve Chapter 8, Code 8.5 /mink
• Arm Move Chapter 8, Code 8.7 /arm
http://cs.smith.edu/~orourke/books/CompGeom/CompGeom.html
• Prerequisites
• Coding experience in C, C++
• Project coding may be done in Java if desired
• Standard CS graduate-level math prerequisites + high school Euclidean geometry
• linear algebra, topology
Growth of Functions Summations Recurrences Sets Probability MATH Proofs Geometry
• Syllabus (current plan) Part 1
• Syllabus (current plan) Part 2
• Important Dates
• Midterm Exam: Wednesday, 3/7
• Open books, open notes
• Final Exam: none
If you have conflicts with exam date, please notify me as soon as possible.
• Homework 35%
• Project 35%
• Midterm (O’Rourke) 30% (open book, notes )
* *Some project writeups may be eligible for submission to a computational geometry conference.
• Machine Accounts
• Each student will have an account on my machine: minkowski.cs.uml.edu.
• 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.
• To transfer files, use a secure FTP (e.g. sftp).
• 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
• VLSI Design:
• Custom layout algorithms for silicon compiler
• Geometric Modeling:
• Partitioning cubic B-spline curves
• Manufacturing:
• see taxonomy on next slide
• 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
• 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