UMass Lowell Computer Science 91.580.201

Geometric Modeling Prof. Karen Daniels

Spring, 2009

Lecture 1Lecture 1Course IntroductionCourse Introduction

Course Introduction

What is Geometric Modeling?What is Geometric Modeling?

Geometric Modeling: 91.580.201 Mondays 5:30-8:30, Prof. Daniels

Methods for representing and manipulating geometric Methods for representing and manipulating geometric objects in a computational setting.objects in a computational setting.

Differential GeometryDifferential Geometry

Computational GeometryComputational Geometry

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

Computer-AidedComputer-Aided Geometric DesignGeometric Design

ConstructiveConstructiveSolid Solid GeometryGeometry

Geometric ModelingGeometric ModelingCourtesy of Cadence Design SystemsCourtesy of Cadence Design Systems

Courtesy of Stanford UniversityCourtesy of Stanford University

Courtesy of Silicon GraphicsCourtesy of Silicon Graphics

Sample Application Areas

Computer GraphicsComputer Graphics

Geographic Geographic Information SystemsInformation Systems& Spatial Databases& Spatial Databases

Medical Medical ImagingImaging

CADCAD

VideoVideoGamesGames

Meshing for Meshing for Finite Element AnalysisFinite Element Analysis

Courtesy of Cadence Design SystemsCourtesy of Cadence Design Systems

CoveringCovering

Topological Invariant Topological Invariant EstimationEstimation

Geometric Model Examples

Source: MortensonSwept SurfaceConstructive Solid Geometry

Courtesy of Silicon GraphicsCourtesy of Silicon Graphics

Model Examples (continued)

Sources: Hill /Kelley OpenGL and Mortenson

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

Model Examples (continued)

Sources: Hill /Kelley OpenGL and Stanford Graphics Lab

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

Meshing for Finite Element AnalysisMeshing for Finite Element Analysis

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

Model Examples (continued)

Courtesy of Silicon GraphicsCourtesy of Silicon Graphics

Rendered TeapotsRendered Teapotsgenerated using OpenGLgenerated using OpenGL

Brief 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: Computer-aided design (CAD) and manufacturing (CAM) begins.1950’s: Computer-aided design (CAD) and manufacturing (CAM) begins.

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:

bicubic patches, piecewise curves and surfacesbicubic patches, piecewise curves and surfaces solid modeling: boundary representation (b-rep) and constructive solid geometrysolid modeling: boundary representation (b-rep) and constructive solid geometry

1980’s: 1980’s: nonuniform rational B-splines (NURBS) take rootnonuniform rational B-splines (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 Introduction

Course DescriptionCourse Description

Web PageWeb Page

http://www.cs.uml.edu/~kdaniels/courses/GEOM_580_S09.html

Nature 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 practice with objects’ properties and representationspractice with objects’ properties and representations

PracticePractice ProgramsPrograms

Course Structure: 2 Parts

Advanced TopicsAdvanced Topics

(to be determined by student interests)(to be determined by student interests)

SplinesSplinesMeshing Meshing Topological PropertiesTopological PropertiesStudent ProjectsStudent Projects

papers from literaturepapers from literature

Courtesy of Cadence Design SystemsCourtesy of Cadence Design Systems

FundamentalsFundamentalsMath and representationsMath and representations

Curves: Bezier, B-splineCurves: Bezier, B-spline

Surfaces: Bezier, B-splineSurfaces: Bezier, B-spline

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

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

Courtesy of Silicon GraphicsCourtesy of Silicon Graphics

Textbooks

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

• by Michael E. Mortensonby Michael E. Mortenson• Curves and Surfaces for CAGD Curves and Surfaces for CAGD

(5(5thth edition) edition)• By Gerald FarinBy Gerald Farin

can be ordered on-line

+ conference, journal papers+ conference, journal papers

Computing Environments

OpenGL C++ graphics library and utilitiesOpenGL C++ graphics library and utilities Linux or PCLinux or PC Open sourceOpen source

Computational Geometry Algorithms Library Computational Geometry Algorithms Library (CGAL) in C++ with templates(CGAL) in C++ with templates Linux or PCLinux or PC Open sourceOpen source

Visit to UML’s Mechanical Engineering Dept. to Visit to UML’s Mechanical Engineering Dept. to view CAD softwareview CAD software

Prerequisites

Graduate Algorithms (91.503) is suggestedGraduate Algorithms (91.503) is suggested Additional helpful course backgroundAdditional helpful course background

computational 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 CGAL

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

Linear AlgebraLinear Algebra SummationsSummations TopologyTopology

SetsSets MATHMATH ProofsProofs GeometryGeometry

Syllabus (current plan)

**

Syllabus (current plan, continued)

**

Grading

No exams Homework 40% Literature Reviews 20%

Lead class discussion Project 40%

Homework

11 M 1/27 M 1/27 M 2/2 Math Basics M 2/2 Math Basics M 2/9 OpenGL example M 2/9 OpenGL example

HW#HW# AssignedAssigned DueDue ContentContent