UMass Lowell Computer Science UMass Lowell Computer Science 91.580.201

Geometric Modeling91.580.201

Geometric ModelingGeometric ModelingProf. Karen Daniels

Spring 2011

Geometric ModelingProf. Karen Daniels

Spring 2011Spring, 2011Spring, 2011

Lecture 1Lecture 1C I t d tiC I t d tiCourse IntroductionCourse Introduction

Course IntroductionCourse Introduction

What is Geometric Modeling?What is Geometric Modeling?

Geometric Modeling: 91.580.201 Th d 5 30 8 15 P f D i lGeometric Modeling: 91.580.201 Th d 5 30 8 15 P f D i lThursdays 5:30-8:15, Prof. DanielsThursdays 5:30-8:15, Prof. Daniels

Methods for representing and manipulating geometric Methods for representing and manipulating geometric p g p g gp g p g gobjects in a computational setting.objects in a computational setting.

Diff ti l G tDiff ti l G tDifferential GeometryDifferential Geometry

ComputerComputer--AidedAidedGeometric DesignGeometric Design

ConstructiveConstructiveSolid Solid GeometryGeometry

Geometric ModelingGeometric ModelingCourtesy of Cadence Design SystemsCourtesy of Cadence Design Systems

GeometryGeometryCourtesy of Stanford UniversityCourtesy of Stanford University

Courtesy of Silicon GraphicsCourtesy of Silicon Graphics

Computational GeometryComputational Geometry

Adapted from:Adapted from: Geometric ModelingGeometric Modeling by Mortensonby Mortenson

Sample Application AreasSample Application Areas

Geographic Geographic Information SystemsInformation Systems& Spatial Databases& Spatial Databases

Medical Medical ImagingImaging

& Spatial Databases& Spatial Databases

CoveringCovering

Computer GraphicsComputer Graphics

VideoVideoGamesGames

Meshing for Meshing for Finite Element AnalysisFinite Element Analysis

Topological Invariant Topological Invariant EstimationEstimation

CADCAD Courtesy of Cadence Design SystemsCourtesy of Cadence Design Systems

Geometric Model ExamplesGeometric Model Examples

Courtesy of Silicon GraphicsCourtesy of Silicon GraphicsCourtesy of Silicon GraphicsCourtesy of Silicon Graphics

Source: MortensonSwept SurfaceConstructive Solid Geometry

Model Examples (continued)Model Examples (continued)

Wireframe and Boundary Representation (BWireframe and Boundary Representation (B--Rep) ModelsRep) ModelsWireframe and Boundary Representation (BWireframe and Boundary Representation (B Rep) ModelsRep) Models

Sources: Hill /Kelley OpenGL and Mortenson

Model Examples (continued)Model Examples (continued)Model Examples (continued)Model Examples (continued)

Unstructured 3D Meshes (Rendered)Unstructured 3D Meshes (Rendered)

Sources: Hill /Kelley OpenGL and Stanford Graphics Lab

Unstructured 3D Meshes (Rendered)Unstructured 3D Meshes (Rendered)

Courtesy of Shu Ye and Cadence Design SystemsCourtesy of Shu Ye and Cadence Design Systems

Meshing for Finite Element AnalysisMeshing for Finite Element Analysis

Model Examples (continued)Model Examples (continued)

Rendered TeapotsRendered Teapotsgenerated using OpenGLgenerated using OpenGL

Courtesy of Silicon GraphicsCourtesy of Silicon Graphics

Brief Historical OverviewBrief Historical Overview

•• Renaissance naval architects in Italy used conic sections for drafting.Renaissance naval architects in Italy used conic sections for drafting.•• Computer development spurs advances, starting in 1950’sComputer development spurs advances, starting in 1950’s

•• Computational progress is accompanied by mathematical foundation.Computational progress is accompanied by mathematical foundation.•• 1950’s: Computer1950’s: Computer--aided design (CAD) and manufacturing (CAM) begins.aided design (CAD) and manufacturing (CAM) begins.

N i ll t ll d (NC) hi ( tti )N i ll t ll d (NC) hi ( tti )•• Numerically controlled (NC) machinery (e.g. cutting)Numerically controlled (NC) machinery (e.g. cutting)•• 1960’s: parametric curves begin replacing “French curves.”1960’s: parametric curves begin replacing “French curves.”•• 1970’s: 1970’s:

•• bicubicbicubic patches, piecewise curves and surfacespatches, piecewise curves and surfacesbicubicbicubic patches, piecewise curves and surfacespatches, piecewise curves and surfaces•• solid modeling: boundary representation (bsolid modeling: boundary representation (b--rep) and constructive solid geometryrep) and constructive solid geometry

•• 1980’s: 1980’s: •• nonuniformnonuniform rational Brational B--splinessplines (NURBS) take root(NURBS) take root•• mesh generation evolves, motivated by fields such as engineering and computer mesh generation evolves, motivated by fields such as engineering and computer

graphicsgraphics•• computational geometry becomes a discipline devoted to design and analysis of computational geometry becomes a discipline devoted to design and analysis of

geometric algorithmsgeometric algorithms•• 1990’s and beyond: increased computational power fuels further evolution1990’s and beyond: increased computational power fuels further evolution

•• tremendous progress in computer graphics (e.g. sophisticated rendering)tremendous progress in computer graphics (e.g. sophisticated rendering)•• meshing with large number of verticesmeshing with large number of vertices

Source: Mortenson & Farin & others

Course IntroductionCourse Introduction

Course DescriptionCourse Description

Web PageWeb Page

http://www.cs.uml.edu/~kdaniels/courses/GEOM_580_S11.html

Nature of the CourseNature of the Course

Elective graduate Computer Science courseElective graduate Computer Science courseTheory and PracticeTheory and Practice

Theory: “PencilTheory: “Pencil--andand--paper” exercisespaper” exercisespractice with objects’ properties and representationspractice with objects’ properties and representations

PracticePracticeProgramsPrograms

Course Structure: 2 PartsCourse Structure: 2 Parts

Advanced TopicsAdvanced Topics(to be determined by student interests)(to be determined by student interests)

FundamentalsFundamentalsMath and representationsMath and representations

SplinesSplinesMeshing Meshing Topological PropertiesTopological Properties

Curves: Bezier, BCurves: Bezier, B--splinesplineSurfaces: Bezier, BSurfaces: Bezier, B--splinesplineSolids: sweep solids CSGSolids: sweep solids CSG Topological PropertiesTopological Properties

Student ProjectsStudent Projects

papers from literaturepapers from literature

Solids: sweep solids, CSG, Solids: sweep solids, CSG, meshing, topological meshing, topological propertiesproperties

Spatial databases (guest Spatial databases (guest lecture)lecture)

Courtesy of Cadence Design SystemsCourtesy of Cadence Design SystemsCourtesy of Silicon GraphicsCourtesy of Silicon Graphics

TextbooksTextbooks

• Required: (see web site for details)•• Geometric Modeling (3Geometric Modeling (3rdrd edition)edition)g (g ( ))

•• by Michael E. by Michael E. MortensonMortenson•• Errata is on Misc. Doc. part of web Errata is on Misc. Doc. part of web

iisitesite•• Curves and Surfaces for CAGD Curves and Surfaces for CAGD

(5(5thth edition)edition)(5(5thth edition)edition)•• By Gerald By Gerald FarinFarin

can be ordered on-line+ conference, journal papers+ conference, journal papers

Computing EnvironmentsComputing Environments

OpenGL C++ graphics library and utilitiesOpenGL C++ graphics library and utilitiesLinux or PCLinux or PCOpen sourceOpen source

Computational Geometry Algorithms Library Computational Geometry Algorithms Library (CGAL) in C++ with templates(CGAL) in C++ with templates(CGAL) in C++ with templates(CGAL) in C++ with templates

Linux or PCLinux or PCOpen sourceOpen source

Guest lecture from UML’s Mechanical Guest lecture from UML’s Mechanical Engineering Dept. with demo of CAD softwareEngineering Dept. with demo of CAD software

PrerequisitesPrerequisites

G d t Al ith (91 503) i t dG d t Al ith (91 503) i t dGraduate Algorithms (91.503) is suggestedGraduate Algorithms (91.503) is suggestedAdditional helpful course backgroundAdditional helpful course background

computational geometry, graphics, visualizationcomputational geometry, graphics, visualizationcomputational geometry, graphics, visualizationcomputational geometry, graphics, visualization

Coding experience in C, C++Coding experience in C, C++Additional helpful coding background: OpenGL and/or CGALAdditional helpful coding background: OpenGL and/or CGALp g g pp g g p

Standard CS graduateStandard CS graduate--level math prerequisites:level math prerequisites:calculus, discrete math calculus, discrete math Additional helpful math background:Additional helpful math background:

SetsSets MATHMATH ProofsProofs GeometryGeometry

Linear AlgebraLinear Algebra SummationsSummations TopologyTopology

SetsSets ProofsProofs GeometryGeometry

Syllabus (current plan)Syllabus (current plan)

**

Syllabus (current plan, continued)Syllabus (current plan, continued)

****

** current plancurrent plan

GradingGrading

• No exams• Homework 40%• Literature Reviews 20%

• Lead class discussion• Project 40%Project 40%

HomeworkHomework

11 ThTh 1/27 1/27 ThTh 2/3 Math Basics2/3 Math BasicsHW#HW# AssignedAssigned DueDue ContentContent

ThTh 2/10 OpenGL example 2/10 OpenGL example