Course Introduction in PDF - Computer Science

cs.uml.edu

Course Introduction in PDF - Computer Science

UMass Lowell Computer Science 91.504

Advanced Algorithms

Computational Geometry

Prof. Karen Daniels

Fall, 2012

Lecture 1

Course Introduction

ti


Course Introduction

What is

Computational Geometry

Began in 1970’s: Efficient geometric algorithms


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


Additional Applications

• Numerous ones in O’Rourke, deBerg

• deBerg application highlights (Chapter 1):

Computer Graphics

• Realistic 3D scenes

• Robotics

• Motion planning

• Geographic Information Systems (GIS)

• Terrain modeling

• CAD/CAM

• Boolean operations on objects

• Other: molecular modeling, pattern recognition.


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

Convex Hull

Voronoi Diagram

New Point

Delaunay Triangulation

source: O’Rourke, Computational Geometry in C


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


Computational Geometry

in Context

Geometry

Applied

Math

Design

Analyze

Computational

Geometry

Efficient

Geometric Algorithms

Apply

Applied Computer Science

Theoretical

Computer

Science


Course Introduction

Course Description


Web Page

http://www.cs.uml.edu/~kdaniels/courses/ALG_504_F12.html


Nature of the Course

• Elective undergraduate/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

i i

Convex Hulls

Voronoi Diagrams

Arrangements

Search/Intersection

Motion Planning

Courtesy of Cadence Design Systems

Advanced Topics

(sample topics)

(may change based on student interests)

Geometric Modeling

Visualization

Clustering

pictures from Skiena, O’Rourke, Daniels

papers from literature


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


Textbook Java Demo Applet

Code function

Chapter pointer

directory

-----------------------------------------------------

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


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


Prerequisites

Graduate Algorithms (91.503) or

Undergraduate Algorithms (91.404)

Coding experience in C, C++

Project coding may be done in Java if desired

Standard d CS graduate-level l math

prerequisites + high school Euclidean

geometry

additional helpful math background:

linear algebra, topology

MATH

Summations

Sets

Proofs

Geometry

Growth of Functions

Probability

Recurrences


Syllabus (current plan)


Syllabus (current plan)


Important Dates

• Midterm Exam: Wednesday, 10/24

• Open books, open notes

• Final Exam:

none

• Project Presentations Wednesday, 12/5

If you have conflicts with exam date, please notify me as soon as possible.


Grading

• Homework 30%

• Paper Discussion 5%

• Project 35%

• Midterm (O’Rourke) 30% (open book, notes )


Homework

HW# Assigned

Due

Content

1 W 9/5 W 9/12 O’Rourke Chapter 1

de Berg Chapters 1, 3.1

CGAL documentation

Start working on installing CGAL on machine of your choice.

Time permitting, if you have not taken 91.503 start reading

Chapter 33 of Cormen’s “Introduction to Algorithms.


Accompanying slides are in Lecture 8 of:

http://www.cs.uml.edu/~kdaniels/courses/ALG_503_S12.html


Course Introduction

My Geometry Related 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

Maximum

Rectangle

Geometric Restriction

Distance-Based

Subdivision

Limited Gaps

Containment

Ordered

Containment

Maximal Cover

Minimal

Enclosure

Two-Phase Layout

Lattice

Packing

Column-Based Layout


to be continued in another slide show

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