Graduate Student Courses
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Fundamentals of Applied
Geometric Modeling
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Time 2003-2011 Winter Quarter (32 Teaching Hours) |
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Description Geometric modeling includes shape
representation and processing. It is fundamentals of computer graphics, CAD,
digital media and entertainment, scientific visualization, GIS, bio-informatics.
The course includes the following contents such as mathematical principles
and fundamentals of geometric modeling, parametric representation, implicit
representation, solid modeling etc. This course is designed for both Ph.D.
students and master students. |
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Preliminary Calculus, Linear algebra, Numerical
analysis, Data structure, C/C++ |
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Examination Project and Report |
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Contents l
Vector and Affine
Spaces 1.
Coordinate Systems 2.
Vector and Affine Spaces 3.
Frames l
Differential Geometry
of Curves 1.
Representation of Curves and Surfaces 2.
Differential Geometry of Curves l
Differential Geometry
of Surfaces (1) 1.
Tangent plane and surface normal 2.
First fundamental form I (metric) 3.
Second fundamental form II (curvature) l
Differential Geometry
of Surfaces(2) 1.
Principal curvatures 2.
Gaussian and mean curvatures 3.
Euler's theorem and Dupin's indicatrix l
Bézier Curves and
Surfaces (1) 1.
Bernstein Polynomials 2.
A Divide-and-Conquer Method for Drawing a Bézier Curve 3.
Quadratic Bézier Curves 4.
Cubic Bézier Curve 5.
A Matrix Representation for Cubic Bézier Curves l
Bézier Curves and
Surfaces (2) 1.
Reparameterizing Bézier Curves 2.
Bézier Control Polygons for a Cubic Curve 3.
The Equations for a Bézier Curve of Arbitrary Degree 4.
Bézier Patches 5.
Bézier Curves on Bézier Patches 6.
Subdivision of Bézier Patches 7.
A Matrix Representation of the Cubic Bézier Patch 8.
Advanced Topics on Bézier Curves/Patches l
B-Spline Curves and
Surfaces (1) 1.
The Analytic and Geometric Definition of a B-Spline
Curve 2.
The Uniform B-Spline Blending Functions 3.
The DeBoor-Cox Calculation l
B-Spline Curves and
Surfaces (2) 1.
Uniform B-Spline Definition: Convolution Form 2.
The Two-Scale Relation for Uniform B-Splines 3.
A Proof of the Two-Scale Relation for Uniform Splines 4.
B-Spline Curves l
B-Spline Curves and
Surfaces (3) 1.
Rational B-Spline Curves 2.
Non-Rational B-Spline Surfaces 3.
Rational B-Spline Surfaces 4.
Catmull-Rom Spline l
B-Spline
Interpolation and Approximation 1.
Parameter Selection and Knot Vector Generation 2.
Global Curve Interpolation 3.
Global Curve Approximation 4.
Global Surface Interpolation 5.
Global Surface Approximation l
Subdivision Curves
and Surfaces (1) 1.
Subdivision/Refinement Process 2.
Chaikin’s Curves 3.
Quadratic Uniform B-Spline Curve Refinement 4.
Cubic Uniform B-Spline Curve Refinement 5.
Vertex and Edge Points 6.
Developing a Matrix Equation for Refinement 7.
Eigen-Analysis for Refinement Matrices 8.
Direct Calculation of Points on Cubic Subdivision Curves
9.
Calculating the Tangent Vectors at a Point l
Subdivision Curves
and Surfaces (2) 1.
Subdivision Methods for Quadratic B-Spline Surfaces 2.
Doo-Sabin Surfaces 3.
Subdivision Methods for Cubic B-Spline Surfaces 4.
Catmull-Clark Surfaces 5.
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Implicit Surface:
Metaball and Quadratic Algebraic Surface 1.
Oveview of implicit surface modeling 2.
Metaball and blobby model 3.
Quadratic algebraic surfaces l
Implicit Surface:
A-patch 1.
Introduction 2.
Mathematical preliminaries 3.
Curvelinear mesh schemes 4.
Simplex- and box-based schemes 5.
Subdivision based schemes l
Implicit Surface:
Displaying implicit surfaces 1.
Surface Tilling 2.
Raytracing 3.
Using Particles to Sample and Control More Complex
Implicit Surfaces l
Solid Modeling 1.
Solid Representations: An Introduction 2.
Wireframe Models 3.
Boundary Representations 4.
Constructive Solid Geometry 5.
References |
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Computer Graphics (With
Prof. Qunsheng Peng)
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Time 2007-2011 Fall and Winter Quarters (64 Teaching
Hours) |
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Description The course will focus on
introductions of fundamental concepts, classical algorithms, research
progress in computer graphics. The topics to be covered are: overview of the
graphics process, rasterization process, transformation and clipping,
geometric modeling, visible surface determination, realistic images
synthesis, fundamental of scientific visualization. This course is designed
for both Ph.D. students and master students. |
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Preliminary Calculus, Linear algebra, Data
structure, C/C++ |
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Examination Project and Report |
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Contents To be added … |