UMass Lowell Computer Science 91.580.201 Geometric Modeling Prof. Karen Daniels Spring, 2009

1. UMass Lowell Computer Science 91.580.201 Geometric ModelingProf. Karen DanielsSpring, 2009 Lecture 1 Course Introduction

2. Course Introduction What is Geometric Modeling?

3. Differential Geometry Computer-Aided Geometric Design Constructive Solid Geometry Geometric Modeling Courtesy of Cadence Design Systems Computational Geometry Courtesy of Stanford University Courtesy of Silicon Graphics Adapted from:Geometric Modeling by Mortenson Geometric Modeling: 91.580.201 Mondays 5:30-8:30, Prof. Daniels Methods for representing and manipulating geometric objects in a computational setting.

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

5. Constructive Solid Geometry Swept Surface Geometric Model Examples Courtesy of Silicon Graphics 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. • 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 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 http://www.cs.uml.edu/~kdaniels/courses/GEOM_580_S09.html

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. Part 1 Part 2 Courtesy of Cadence Design Systems Course Structure: 2 Parts Advanced Topics (to be determined by student interests) Splines Meshing Topological Properties Student Projects Fundamentals Math and representations Curves: Bezier, B-spline Surfaces: Bezier, B-spline Solids: sweep solids, CSG, meshing, topological properties Spatial databases (guest lecture) papers from literature Courtesy of Silicon Graphics

14. 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

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: MATH Sets Geometry Proofs Summations Linear Algebra Topology

17. Syllabus (current plan) Part 1 *

18. Syllabus (current plan, continued) Part 2 *

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

20. Homework HW# Assigned DueContent 1 M 1/27 M 2/2 Math Basics M 2/9 OpenGL example