Part 1 - Computer Science

UMass Lowell Computer Science91.580.201Geometric ModelingProf. Karen DanielsSpring, 2011Lecture 1Course Introductionti

Course IntroductionWhat is Geometric Modeling?

Geometric Modeling: 91.580.201Thursdays 5:30-8:15, 815 Prof. DanielsMethods for representing and manipulating gggeometricobjects in a computational setting.Differential GeometryConstructiveSolidGeometryCourtesy of Cadence Design SystemsGeometric ModelingCourtesy of Stanford UniversityComputer-AidedGeometric DesignComputational GeometryCourtesy of Silicon GraphicsAdapted from: Geometric Modeling by Mortenson

Sample Application AreasMedicalImagingGeographicInformation Systems& Spatial DatabasesCoveringVideoGamesComputer GraphicsMeshing forFinite Element AnalysisTopological InvariantEstimationCADCourtesy of Cadence Design Systems

Geometric Model ExamplesCourtesy of Silicon GraphicsSwept SurfaceConstructive Solid GeometrySource: Mortenson

Model Examples (continued)Wireframe and Boundary Representation (B-Rep) ModelsSources: Hill /Kelley OpenGL and Mortenson

Model Examples (continued)Unstructured 3D Meshes (Rendered)Sources: Hill /Kelley OpenGL and Stanford Graphics LabMeshing for Finite Element AnalysisCourtesy of Shu Ye and Cadence Design Systems

Model Examples (continued)Rendered Teapotsgenerated using OpenGLCourtesy of Silicon Graphics

Brief Historical Overview• Renaissance naval architects in Italy used conic sections for drafting.• Computer development spurs advances, starting in 1950’s• Computational progress is accompanied by mathematical foundation.• 1950’s: Computer-aided design (CAD) and manufacturing (CAM) begins.• Numerically controlled (NC) machinery (e.g. cutting)• 1960’s: parametric curves begin replacing “French curves.”• 1970’s:• bicubic patches, piecewise curves and surfaces• solid modeling: boundary representation (b-rep) and constructive solid geometry• 1980’s:• nonuniform rational B-splines(NURBS) take root• mesh generation evolves, motivated by fields such as engineering and computergraphics• computational geometry becomes a discipline devoted to design and analysis ofgeometric algorithms• 1990’s and beyond: increased computational power fuels further evolution• tremendous progress in computer graphics (e.g. sophisticated rendering)• meshing with large number of verticesSource: Mortenson & Farin & others

Course IntroductionCourse Description

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

Nature of the Course Elective graduate Computer Science course Theory and Practice Theory: “Pencil-and-paper” exercises practice with objects’ properties and representations Practice Programs

Course Structure: 2 PartsFundamentalsMath and representationsCurves: Bezier, B-splineSurfaces: Bezier, B-splineSolids: sweep solids, CSG,meshing, topologicalpropertiesSpatial databases (guestlecture)Advanced Topics(to be determined by student interests)SplinesMeshingTopological PropertiesStudent Projectspapers from literatureCourtesy of Silicon GraphicsCourtesy of Cadence Design Systems

Textbooks• Required: (see web site for details)• Geometric Modeling g( (3 rd edition)• by Michael E. Mortenson• Errata is on Misc. Doc. part of website• Curves and Surfaces for CAGD(5 th edition)• By Gerald Farincan be ordered on-line+ conference, journal papers

Computing Environments OpenGL C++ graphics library and utilities Linux or PC Open source Computational Geometry Algorithms Library(CGAL) in C++ with templates Linux or PC Open source Guest lecture from UML’s MechanicalEngineering Dept. with demo of CAD software

Prerequisites Graduate Algorithms (91.503) is suggested Additional helpful course background computational geometry, graphics, visualization Coding experience in C, C++ Additional helpful coding background: OpenGL and/or CGAL Standard CS graduate-level math prerequisites: calculus, discrete math Additional helpful math background:SetsMATHProofsGeometryLinear AlgebraSummationsTopology

Syllabus (current plan)*

Syllabus (current plan, continued)**current plan

Grading• No exams• Homework 40%• Literature Reviews 20%• Lead class discussion• Project 40%

HomeworkHW# AssignedDueContent1 Th 1/27 Th 2/3 Math BasicsTh 2/10 OpenGL example