Undergraduate Student Course
l
Fundamental of C Programming Language (In Chinese)
http://www.cad.zju.edu.cn/home/jqfeng/c/clang.htm
Graduate Student Courses
l
Fundamentals of Applied Geometric Modeling
|
Time 2003-2019 Fall
Quarter (32 Teaching Hours) |
|
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. |
|
Preliminary Calculus, Linear algebra, Numerical analysis, Data
structure, C/C++ |
|
Examination Project and Report |
|
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.
l
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.
Curve
linear 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 |
l
Computer Graphics
|
Time 2007-2019 Fall
and Winter Quarters (64 Teaching Hours) |
|
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. |
|
Preliminary Calculus, Linear algebra, Data structure, C/C++ |
|
Examination Project and Report |
|
|