7/25/2019 GEOM Lecture1a S11

1/20

UMass Lowell Computer ScienceUMass Lowell Computer Science91.580.20191.580.201

Prof. Karen Daniels

Prof. Karen Daniels,,

Lecture 1 Lecture 1

ourse n ro uc onourse n ro uc on

7/25/2019 GEOM Lecture1a S11

2/20

Course IntroductionCourse Introduction

What is Geometric Modeling?What is Geometric Modeling?

7/25/2019 GEOM Lecture1a S11

3/20

Geometric Modeling : 91.580.201

Geometric Modeling : 91.580.201

urs ays : - : , ro . an e surs ays : - : , ro . an e sMethods for re resentin and mani ulatin eometricMethods for re resentin and mani ulatin eometric

objects in a computational setting.objects in a computational setting.eren a eome ryeren a eome ry

Computer Computer- -Aided AidedGeometric DesignGeometric Design

ConstructiveConstructiveSolidSolidGeometr Geometr

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

Computational GeometryComputational Geometry

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

7/25/2019 GEOM Lecture1a S11

4/20

Sample Application AreasSample Application Areas

GeographicGeographicInformation SystemsInformation Systems

MedicalMedicalImagingImaging

CoveringCovering

Computer GraphicsComputer Graphics

VideoVideoGamesGames

Meshing forMeshing forFinite Element AnalysisFinite Element Analysis

Topological InvariantTopological InvariantEstimationEstimation

CADCAD Courtesy of Cadence Design SystemsCourtesy of Cadence Design Systems

7/25/2019 GEOM Lecture1a S11

5/20

Geometric Model ExamplesGeometric Model Examples

Source: MortensonSwept SurfaceConstructive Solid Geometry

7/25/2019 GEOM Lecture1a S11

6/20

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

Sources: Hill /Kelley OpenGL and Mortenson

7/25/2019 GEOM Lecture1a S11

7/20

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

7/25/2019 GEOM Lecture1a S11

8/20

Model Examples (continued)Model Examples (continued)

Rendered TeapotsRendered Teapotsgenerated using OpenGLgenerated using OpenGL

Courtesy of Silicon GraphicsCourtesy of Silicon Graphics

7/25/2019 GEOM Lecture1a S11

9/20

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 1950sComputer development spurs advances, starting in 1950s

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

umer ca y con ro e mac nery e.g. cu ngumer ca y con ro e mac nery e.g. cu ng 1960s: parametric curves begin replacing French curves.1960s: parametric curves begin replacing French curves.

1970s:1970s: solid modeling: boundary representation (bsolid modeling: boundary representation (b- -rep) and constructive solid geometryrep) and constructive solid geometry

1980s:1980s: nonuniformnonuniform rational Brational B--splinessplines (NURBS) take root(NURBS) take root

mesh generation evolves, motivated by fields such as engineering and computermesh generation evolves, motivated by fields such as engineering and computergraphicsgraphics computational geometry becomes a discipline devoted to design and analysis ofcomputational geometry becomes a discipline devoted to design and analysis of

geometric algorithmsgeometric algorithms 1990s and beyond: increased computational power fuels further evolution1990s 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

7/25/2019 GEOM Lecture1a S11

10/20

Course IntroductionCourse Introduction

Course DescriptionCourse Description

7/25/2019 GEOM Lecture1a S11

11/20

Web PageWeb Page

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

7/25/2019 GEOM Lecture1a S11

12/20

Nature of the Course Nature of the Course

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

Theory: PencilTheory: Pencil- -and and--paper exercises paper exercises practice with objects properties and representations practice with objects properties and representations

PracticePracticeProgramsPrograms

7/25/2019 GEOM Lecture1a S11

13/20

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 representationsSplinesSplines

MeshingMeshingTo olo ical Pro ertiesTo olo ical Pro erties

Curves: Bezier, BCurves: Bezier, B- -splinespline

Surfaces: Bezier, BSurfaces: Bezier, B- -splinespline

Student ProjectsStudent Projects

papers from literaturepapers from literature

, ,, ,meshing, topologicalmeshing, topological

properties properties

Spatial databases (guestSpatial databases (guestlecture)lecture)

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

7/25/2019 GEOM Lecture1a S11

14/20

TextbooksTextbooks

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

by Michael E. by Michael E. MortensonMortenson

Errata is on Misc. Doc. part of webErrata is on Misc. Doc. part of webs tes te Curves and Surfaces for CAGDCurves and Surfaces for CAGD

By GeraldBy Gerald FarinFarin

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

7/25/2019 GEOM Lecture1a S11

15/20

Computing EnvironmentsComputing Environments

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

Computational Geometry Algorithms LibraryComputational Geometry Algorithms Library

Linux or PCLinux or PCOpen sourceOpen source

Guest lecture from UMLs MechanicalGuest lecture from UMLs MechanicalEngineering Dept. with demo of CAD softwareEngineering Dept. with demo of CAD software

7/25/2019 GEOM Lecture1a S11

16/20

PrerequisitesPrerequisitesra ua e gor ms . s sugges era ua e gor ms . s sugges e

Additional helpful course background Additional helpful course background

Coding experience in C, C++Coding experience in C, C++Additional hel ful codin back round: O enGL and/or CGALAdditional hel ful codin back round: O enGL and/or CGAL

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

MATHMATH

Linear AlgebraLinear Algebra SummationsSummations TopologyTopology

roo sroo s

7/25/2019 GEOM Lecture1a S11

17/20

Syllabus (current plan)Syllabus (current plan)

**

7/25/2019 GEOM Lecture1a S11

18/20

Syllabus(current plan, continued)

Syllabus(current plan, continued)

** current plancurrent plan

7/25/2019 GEOM Lecture1a S11

19/20

GradingGrading

No exams Homework 40%

Literature Reviews 20% Lead class discussion

7/25/2019 GEOM Lecture1a S11

20/20