UMass Lowell Computer Science

91.580.201

Geometric ModelingProf. Karen Daniels

Spring, 2009

Lecture 1

Course Introduction

Course Introduction

What is Geometric Modeling?

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

Methods for representing and manipulating geometric

objects in a computational setting.

Differential Geometry

Computational Geometry

Adapted from: Geometric Modeling by Mortenson

Computer-Aided

Geometric Design

Constructive

Solid

Geometry

Geometric ModelingCourtesy of Cadence Design Systems

Courtesy of Stanford University

Courtesy of Silicon Graphics

Sample Application Areas

Computer Graphics

Geographic

Information Systems

& Spatial Databases

Medical

Imaging

CAD

Video

Games

Meshing for

Finite Element Analysis

Courtesy of Cadence Design Systems

Covering

Topological Invariant

Estimation

Geometric Model Examples

Source: MortensonSwept SurfaceConstructive Solid Geometry

Courtesy of Silicon Graphics

Model Examples (continued)

Sources: Hill /Kelley OpenGL and Mortenson

Wireframe and Boundary Representation (B-Rep) Models

Model Examples (continued)

Sources: Hill /Kelley OpenGL and Stanford Graphics Lab

Courtesy of Shu Ye and Cadence Design Systems

Meshing for Finite Element Analysis

Unstructured 3D Meshes (Rendered)

Model Examples (continued)

Courtesy of Silicon Graphics

Rendered Teapots

generated using OpenGL

Brief Historical Overview

Renaissance naval architects in Italy used conic sections for drafting.

Computer development spurs advances, starting in 1950s Computational progress is accompanied by mathematical foundation.

1950s: Computer-aided design (CAD) and manufacturing (CAM) begins. Numerically controlled (NC) machinery (e.g. cutting)

1960s: parametric curves begin replacing French curves.

1970s: bicubic patches, piecewise curves and surfaces

solid modeling: boundary representation (b-rep) and constructive solid geometry

1980s: nonuniform rational B-splines (NURBS) take root

mesh generation evolves, motivated by fields such as engineering and computer graphics

computational geometry becomes a discipline devoted to design and analysis of geometric algorithms

1990s 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 Introduction

Course Description

Web Page

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

Advanced Topics(to be determined by student interests)

Splines

Meshing

Topological Properties

Student Projects

papers from literature

Courtesy of Cadence Design Systems

Fundamentals

Math and representations

Curves: Bezier, B-spline

Surfaces: Bezier, B-spline

Solids: sweep solids, CSG,

meshing, topological

properties

Spatial databases (guest

lecture)

Courtesy of Silicon Graphics

Textbooks

Required: (see web site for details)

Geometric Modeling (3rd edition) by Michael E. Mortenson

Curves and Surfaces for CAGD (5th edition) By Gerald Farin

can 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

Visit to UMLs Mechanical Engineering Dept. to view 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:

Linear Algebra Summations Topology

Sets MATH Proofs Geometry

Syllabus (current plan)

*

M 1/26

Syllabus (current plan, continued)

*

Grading

No exams

Homework 40%

Literature Reviews 20%

Lead class discussion

Project 40%

Homework

1 M 1/26 M 2/2 Math Basics

M 2/9 OpenGL example

HW# Assigned Due Content