UMass Lowell Computer Science 91.504 Advanced Algorithms

Computational Geometry Prof. Karen Daniels

Spring, 2007

UMass Lowell Computer Science 91.504 Advanced Algorithms

Computational Geometry Prof. Karen Daniels

Spring, 2007

Lecture 1Lecture 1

Course IntroductionCourse Introduction

Course IntroductionCourse Introduction

What is What is

Computational Geometry?Computational Geometry?

Advanced AlgorithmsComputational Geometry

Advanced AlgorithmsComputational Geometry

TelecommunicationsTelecommunications

VisualizationVisualization

91.504

ManufacturingManufacturing

Computer Computer GraphicsGraphics

Design Analyze

Apply

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Sample Application AreasSample Application Areas

Computer GraphicsComputer Graphics

Geographic Geographic Information SystemsInformation Systems

RoboticsRobotics

BioinformaticsBioinformatics

AstrophysicsAstrophysics

Medical Medical ImagingImaging

TelecommunicationsTelecommunications

Data Mining & Data Mining & VisualizationVisualization

Typical ProblemsTypical Problems

bin packingbin packing

Voronoi diagramVoronoi diagram simplifying simplifying

polygonspolygons

shape similarityshape similarity

convex hullconvex hull

maintaining line maintaining line arrangementsarrangements

polygon partitioningpolygon partitioning nearest neighbor nearest neighbor

searchsearch

kd-treeskd-trees

SOURCESOURCE: Steve Skiena’s Algorithm Design Manual : Steve Skiena’s Algorithm Design Manual

(for problem descriptions, see graphics gallery at (for problem descriptions, see graphics gallery at http://www.cs.sunysb.edu/~algorith))

Common Computational Geometry StructuresCommon Computational Geometry Structures

Voronoi DiagramVoronoi DiagramConvex HullConvex Hull

New PointNew Point

source: O’Rourke, Computational Geometry in Csource: O’Rourke, Computational Geometry in C

Delaunay TriangulationDelaunay Triangulation

Sample Tools of the TradeSample Tools of the Trade

Algorithm Design Patterns/Techniques:Algorithm Design Patterns/Techniques:binary searchbinary search divide-and-conquerdivide-and-conquer dualitydualityrandomizationrandomization sweep-linesweep-linederandomizationderandomization parallelismparallelism

Algorithm Analysis Techniques:Algorithm Analysis Techniques:asymptotic analysis, amortized analysisasymptotic analysis, amortized analysis

Data Structures:Data Structures:winged-edge, quad-edge, winged-edge, quad-edge, range tree, kd-treerange tree, kd-tree

Theoretical Computer ScienceTheoretical Computer Science principles:principles:NP-completeness, hardnessNP-completeness, hardness

Growth of FunctionsGrowth of Functions

SummationsSummations

RecurrencesRecurrences

SetsSets

ProbabilityProbability

MATHMATH ProofsProofs GeometryGeometry

Graph TheoryGraph TheoryCombinatoricsCombinatorics

Linear AlgebraLinear Algebra

Computational Geometryin Context

Computational Geometryin Context

TheoreticalTheoreticalComputerComputer

ScienceScience

Applied Computer ScienceApplied Computer Science

AppliedAppliedMathMath

GeometryGeometry

ComputationalComputationalGeometryGeometry

Efficient Efficient Geometric AlgorithmsGeometric Algorithms

Design Analyze

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Course IntroductionCourse Introduction

Course DescriptionCourse Description

Web PageWeb Page

http://www.cs.uml.edu/~kdaniels/courses/ALG_504.html

Nature of the CourseNature of the Course

Elective graduate Computer Science courseElective graduate Computer Science course Theory and PracticeTheory and Practice

Theory: “Pencil-and-paper” exercisesTheory: “Pencil-and-paper” exercises design an algorithmdesign an algorithm analyze its complexityanalyze its complexity modify an existing algorithmmodify an existing algorithm prove propertiesprove properties

PracticePractice ProgramsPrograms Real-world examplesReal-world examples

Course Structure: 2 PartsCourse Structure: 2 Parts

BasicsBasicsPolygon TriangulationPolygon Triangulation

PartitioningPartitioning

Convex HullsConvex Hulls

Voronoi DiagramsVoronoi Diagrams

ArrangementsArrangements

Search/IntersectionSearch/Intersection

Motion PlanningMotion Planning

Advanced TopicsAdvanced Topics (sample topics)(sample topics)

(may change based on student interests)(may change based on student interests)

Covering Covering

ClusteringClustering

PackingPacking Geometric ModelingGeometric Modeling

Topological EstimationTopological Estimation

papers from literaturepapers from literature

TextbookTextbook

Required: Computational Geometry in CComputational Geometry in C

second editionsecond edition by Joseph O’Rourkeby Joseph O’RourkeCambridge University PressCambridge University Press19981998 see course web site for ISBN number(s) & errata listsee 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+ conference, journal papers

Textbook Java Demo AppletTextbook Java Demo Applet

Code functionCode function Chapter pointerChapter pointer directorydirectory----------------------------------------------------------------------------------------------------------TriangulateTriangulate Chapter 1, Code 1.14Chapter 1, Code 1.14 /tri/tri

Convex Hull(2D)Convex Hull(2D) Chapter 3,Chapter 3, Code 3.8Code 3.8 /graham/graham

Convex Hull(3D)Convex Hull(3D) Chapter 4, Code 4.8Chapter 4, Code 4.8 /chull/chullsphere.csphere.c Chapter 4, Fig. 4.15Chapter 4, Fig. 4.15 /sphere/sphereDelaunay Triang Delaunay Triang Chapter 5, Code 5.2Chapter 5, Code 5.2 /dt/dtSegSegIntSegSegInt Chapter 7, Code 7.2Chapter 7, Code 7.2 /segseg/segsegPoint-in-polyPoint-in-poly Chapter 7, Code 7.13Chapter 7, Code 7.13 /inpoly/inpolyPoint-in-hedronPoint-in-hedron Chapter 7, Code 7.15Chapter 7, Code 7.15 /inhedron/inhedronInt Conv PolyInt Conv Poly Chapter 7, Code 7.17Chapter 7, Code 7.17 /convconv/convconvMink ConvolveMink Convolve Chapter 8, Code 8.5Chapter 8, Code 8.5 /mink/minkArm Move Arm Move Chapter 8, Code 8.7Chapter 8, Code 8.7 /arm/arm

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

PrerequisitesPrerequisites

Graduate Algorithms (91.503)Graduate Algorithms (91.503) Coding experience in C, C++Coding experience in C, C++

Project coding may be done in Java if desiredProject coding may be done in Java if desired Standard CS graduate-level math Standard CS graduate-level math

prerequisites + high school Euclidean prerequisites + high school Euclidean geometrygeometry additional helpful math background:additional helpful math background:

linear algebra, topologylinear algebra, topology

Growth of FunctionsGrowth of Functions

SummationsSummations

RecurrencesRecurrences

SetsSets

ProbabilityProbability

MATHMATHProofsProofs GeometryGeometry

Syllabus (current plan)Syllabus (current plan)

Syllabus (current plan)Syllabus (current plan)

Important DatesImportant Dates

Midterm Exam:Midterm Exam: Wednesday, 3/7Wednesday, 3/7 Open books, open notesOpen books, open notes

Final Exam:Final Exam: nonenone

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

GradingGrading

Homework 35% Project 35% Midterm (O’Rourke) 30% (open book,

notes )

**

*Some project writeups may be eligible for submission *Some project writeups may be eligible for submission to a computational geometry conference.to a computational geometry conference.

Machine AccountsMachine Accounts

Each student will have an account on my machine: Each student will have an account on my machine: minkowski.cs.uml.edu.minkowski.cs.uml.edu.

Username will be the same as your username on CS. Username will be the same as your username on CS. Password will be your initials followed by the last 5 Password will be your initials followed by the last 5

digits on the bottom right hand corner of the back of digits on the bottom right hand corner of the back of your student id card.your student id card.

To remotely log in, use a secure shell (e.g. ssh).To remotely log in, use a secure shell (e.g. ssh). To transfer files, use a secure FTP (e.g. sftp).To transfer files, use a secure FTP (e.g. sftp). LEDA and CGAL libraries are on minkowski.LEDA and CGAL libraries are on minkowski.

HomeworkHomework

11 W 1/24 W 1/24 W 2/7 O’Rourke Chapter 1 W 2/7 O’Rourke Chapter 1

HW#HW# AssignedAssigned DueDue ContentContent

Course IntroductionCourse Introduction

My Computational Geometry ResearchMy Computational Geometry Research

My Previous Applied Algorithms ResearchMy Previous Applied Algorithms Research

VLSI Design:VLSI Design: Custom layout Custom layout

algorithms for silicon algorithms for silicon compilercompiler

Geometric Modeling:Geometric Modeling: Partitioning cubic B-Partitioning cubic B-

spline curvesspline curves

Manufacturing:Manufacturing: see taxonomy on next see taxonomy on next

slideslide

Taxonomy of ProblemsSupporting Apparel Manufacturing

Taxonomy of ProblemsSupporting Apparel Manufacturing

Ordered Ordered ContainmentContainment

Geometric RestrictionGeometric Restriction

Distance-Based Distance-Based SubdivisionSubdivision

Maximum Maximum RectangleRectangle

Limited GapsLimited Gaps

Minimal Minimal EnclosureEnclosure

Column-Based LayoutColumn-Based LayoutTwo-Phase LayoutTwo-Phase Layout

Lattice Lattice PackingPacking

ContainmentContainment

Maximal CoverMaximal Cover

My Applied Algorithms Research Focus at UMass Lowell

My Applied Algorithms Research Focus at UMass Lowell

TelecommunicationsTelecommunications

Data Mining, Data Mining, Visualization, Visualization, BioinformaticsBioinformatics

ManufacturingManufacturing

Design Analyze

Apply

for for covering, assignment, clustering, packing, layoutcovering, assignment, clustering, packing, layout

feasibility, optimization problemsfeasibility, optimization problems

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