geom lecture
DESCRIPTION
Geometric modelling lecture by Michael E. MortensonTRANSCRIPT
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UMass Lowell Computer Science
91.580.201
Geometric ModelingProf. Karen Daniels
Spring, 2009
Lecture 1
Course Introduction
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Course Introduction
What is Geometric Modeling?
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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
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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
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Geometric Model Examples
Source: MortensonSwept SurfaceConstructive Solid Geometry
Courtesy of Silicon Graphics
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Model Examples (continued)
Sources: Hill /Kelley OpenGL and Mortenson
Wireframe and Boundary Representation (B-Rep) Models
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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)
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Model Examples (continued)
Courtesy of Silicon Graphics
Rendered Teapots
generated using OpenGL
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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
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Course Introduction
Course Description
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Web Page
http://www.cs.uml.edu/~kdaniels/courses/GEOM_580_S09.html
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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
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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
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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
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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
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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
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Syllabus (current plan)
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M 1/26
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Syllabus (current plan, continued)
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Grading
No exams
Homework 40%
Literature Reviews 20%
Lead class discussion
Project 40%
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Homework
1 M 1/26 M 2/2 Math Basics
M 2/9 OpenGL example
HW# Assigned Due Content