Supporting Apparel Manufacturing

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
Advanced Topics
(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
Graduate Algorithms (91.503)
Coding experience in C, C++
Project coding may be done in Java if desired
Standard CS graduate-level math prerequisites + high school Euclidean geometry
additional helpful math background:
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.

Grading
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.
Username will be the same as your username on CS.
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 remotely log in, use a secure shell (e.g. ssh).
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

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