Course Introduction in PDF - Computer Science

UMass Lowell Computer Science 91.504

Advanced Algorithms

Computational Geometry

Prof. Karen Daniels

Spring, 2010

Lecture 1

Course Introduction

ti

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Course Introduction

What is

Computational Geometry

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Advanced Algorithms

Computational Geometry

Computer

Graphics

Design Analyze

feasibility, estimation, optimization problems

Visualization

for

covering, assignment, clustering, packing, layout,

geometric modeling

Covering for

Geometric

Modeling

Data Mining,

Clustering, for

Bioinformatics

Packing for Manufacturing

Apply

Courtesy of Cadence Design Systems

Meshing

for

Geometric

Modeling

CAD

Topological Invariant

Estimation for

Geometric Modeling

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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)

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Common Computational

Geometry Structures

Convex Hull

Voronoi Diagram

New Point

Delaunay Triangulation

source: O’Rourke, Computational Geometry in C

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Sample Tools of the Trade

Algorithm Design Patterns/Techniques:

binary search

randomization

derandomization

divide-and-conquer

sweep-line

parallelism

Algorithm Analysis Techniques:

asymptotic analysis, amortized analysis

Data Structures:

duality

winged-edge, edge, quad-edge,

range tree, kd-tree

Theoretical Computer Science principles:

i NP-completeness, hardness

Sets

MATH

Summations

Growth of Functions

Combinatorics

Probability

Proofs

Linear Algebra

Graph Theory

Geometry

Recurrences

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Computational Geometry

in Context

Geometry

Applied

Math

Design

Analyze

Computational

Geometry

Efficient

Geometric Algorithms

Apply

Applied Computer Science

Theoretical

Computer

Science

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Course Introduction

Course Description

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Web Page

http://www.cs.uml.edu/~kdaniels/courses/ALG_504_S10.html

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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

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Course Structure: 2 Parts

Basics

Polygon Triangulation

Partitioning

i i

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

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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

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Textbook Java Demo Applet

Code function

Chapter pointer

directory

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Triangulate Chapter 1, Code 1.14

/tri

Convex Hull(2D) Chapter 3, Code 3.8

Convex Hull(3D) Chapter 4, Code 4.8

sphere.c Chapter 4, Fig. 4.15

Delaunay Triang Chapter 5, Code 5.2

SegSegInt Chapter 7, Code 7.2

Point-in-poly

Chapter 7, Code 7.13

Point-in-hedron

Chapter 7, Code 7.15

Int Conv Poly Chapter 7, Code 7.17

Mink Convolve Chapter 8, Code 8.5

Arm Move Chapter 8, Code 8.7

/graham

/chull

/sphere

/dt

/segseg

/inpoly

/inhedron

/convconv

/mink

/arm

http://cs.smith.edu/~orourke/books/CompGeom/CompGeom.html

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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

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Prerequisites

Graduate Algorithms (91.503)

Coding experience in C, C++

Project coding may be done in Java ifd desired

d

Standard CS graduate-level math

prerequisites it + high h school Euclidean

geometry

additional helpful math background:

linear algebra, topology

MATH

Summations

Sets

Proofs

Geometry

Growth of Functions

Probability

Recurrences

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Syllabus (current plan)

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Syllabus (current plan)

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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.

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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.

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Homework

HW# Assigned

Due

Content

1 Th 1/28 Th 2/11 O’Rourke Chapters 1,2

de Berg Chapters 1, 3

CGAL documentation

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Course Introduction

My Geometry Related Research

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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

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Taxonomy of Problems

Supporting Apparel Manufacturing

Maximum

Rectangle

Geometric Restriction

Distance-Based

Subdivision

Limited Gaps

Containment

Ordered

Containment

Maximal Cover

Minimal

Enclosure

Two-Phase Layout

Lattice

Packing

Column-Based Layout

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to be continued in another slide show