UMass Lowell Computer Science Geometric Modeling Prof. Karen Daniels Spring, 2009 Lecture 1 Course Introduction

What is Geometric Modeling?

Geometric Modeling : 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 Geometric Design ConstructiveSolidGeometry Geometric Modeling Courtesy of Cadence Design Systems Courtesy of Stanford University Courtesy of Silicon Graphics

Sample Application Areas Computer Graphics Geographic Information Systems & Spatial Databases MedicalImaging CAD VideoGames Meshing for Finite Element Analysis Courtesy of Cadence Design Systems Covering Topological Invariant Estimation

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

Course Introduction Course Description

Web Page

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

Course Structure: 2 Parts Advanced Topics (to be determined by student interests) SplinesMeshing 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 (3 rd edition)Geometric Modeling (3 rd edition) by Michael E. Mortensonby Michael E. Mortenson Curves and Surfaces for CAGD (5 th edition)Curves and Surfaces for CAGD (5 th edition) By Gerald FarinBy Gerald Farin can be ordered on-line + conference, journal papers

Computing Environments ä OpenGL C++ graphics library and utilities ä Linux or PC ä Open source ä Computational Geometry Algorithms Library (CGAL) in C++ with templates ä Linux or PC ä Open source ä Visit to UML’s Mechanical Engineering Dept. to view CAD software

Prerequisites ä Graduate Algorithms (91.503) is suggested ä Additional helpful course background ä computational geometry, graphics, visualization ä Coding experience in C, C++ ä Additional helpful coding background: OpenGL and/or CGAL ä Standard CS graduate-level math prerequisites: ä calculus, discrete math ä Additional helpful math background: Linear Algebra Summations Topology Sets MATH Proofs Geometry

Syllabus (current plan) *

Syllabus (current plan, continued) *

Grading ä ä No exams ä ä Homework40% ä ä Literature Reviews20% ä ä Lead class discussion ä ä Project40%

Homework 1 M 1/27 M 2/2 Math Basics M 2/9 OpenGL example M 2/9 OpenGL example HW# Assigned Due Content