Lecture 1 Course Introduction

Transcription

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

2 Course Introduction What is Geometric Modeling?

3 Adapted from: Geometric Modeling by Mortenson Geometric Modeling: Mondays 5:30-8:30, Prof. Daniels Methods for representing and manipulating geometric objects in a computational setting. Differential Geometry Constructive Solid Geometry Courtesy of Cadence Design Systems Geometric Modeling Courtesy of Stanford University Computer-Aided Geometric Design Computational Geometry Courtesy of Silicon Graphics

4 Sample Application Areas Medical Imaging Geographic Information Systems & Spatial Databases Covering Video Games Computer Graphics Meshing for Finite Element Analysis Topological Invariant Estimation CAD Courtesy of Cadence Design Systems

5 Geometric Model Examples Courtesy of Silicon Graphics Swept Surface Constructive Solid Geometry Source: Mortenson

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

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

8 Model Examples (continued) Rendered Teapots generated using OpenGL Courtesy of Silicon Graphics

9 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 s: Computer-aided design (CAD) and manufacturing (CAM) begins. Numerically controlled (NC) machinery (e.g. cutting) 1960 s: parametric curves begin replacing French curves 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 computer graphics computational geometry becomes a discipline devoted to design and analysis of geometric 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 vertices Source: Mortenson & Farin & others

10 Course Introduction Course Description

11 Web Page

12 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

13 Course Structure: 2 Parts Fundamentals Math and representations Curves: Bezier, B-spline Surfaces: Bezier, B-spline Solids: sweep solids, CSG, meshing, topological properties Spatial databases (guest lecture) Advanced Topics (to be determined by student interests) Splines Meshing Topological Properties Student Projects papers from literature Courtesy of Silicon Graphics Courtesy of Cadence Design Systems

14 Textbooks Required: (see web site for details) Geometric Modeling (3 rd edition) by Michael E. Mortenson Curves and Surfaces for CAGD (5 th edition) By Gerald Farin can be ordered on-line + conference, journal papers

15 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 UML s Mechanical Engineering Dept. to view CAD software

16 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: Sets MATH Proofs Geometry Linear Algebra Summations Topology

17 Syllabus (current plan) M 1/26 *

18 * Syllabus (current plan, continued)

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

20 Homework HW# Assigned Due Content 1 M 1/26 M 2/2 Math Basics M 2/9 OpenGL example