Math 155B - Introduction to Computer Graphics, II
Winter 2005.   Univ. of California, San Diego


Due Dates, Lecture Topics & Readings in the Textbook:
The calendar will be updated on a regular basis.
The schedule is subject to changes announced in class.
Monday Wednesday Friday
Week 1
1/3 - 1/7
Hermite polynomials.
Piecewise Bezier curves.
Sections VII.4 & 5.  Review VII.1
C1- and G1-continuity
Catmull-Rom, Overhauser splines.
Sections VII.4, 15.1 & 15.2.
Bezier Curves of degree k.
Convex hulls, other properties.
Sections VII. 6 & 7.
Week 2
1/10 - 1/14
DeCasteljau algorithm.
Recursive subdivision. Degree elevation.
Sections VII.2, 3, 7, 8 & 9.
OpenGL commands  Bezier Patches. 
C1- and G1-continuity.
Sections VII.10 & 11.
Subdividing Bezier patches.
Rational Bezier curves and surfaces.
Sections VII.12, VII.13.
Week 3
1/17 - 1/21
Martin Luther King holiday Circular Bezier curve.  Conic sections.
 Surface of Revolution.
Sections VII.13, VII.14. 
Program #1 due
Circular Disks with Bezier patches
Variation diminishing property.
Other properties. B-Splines overview.
Week 4
1/24 - 1/28
Raytracing overview.  Local/global..
Shadow feelers. Reflection, transmission.
Sections IX.1, IX.1.1.
Transmission rays. Snell's Law.
More local lighting.
Section IX.1 (whole section)
Program #2 due
Advanced ray tracing.
Section IX.2.
Week 5
1/31 - 2/4
Advanced ray tracing, cont'd.
Section IX.2
RayTrace software. (Appendix B)
Tricks to avoid ray tracing.
Project #3 (3DS) due
No class
Week 6
2/7 - 2/11
Sampling lights, Beer's law.
Illumination and photon maps.
Shadow maps.  Shadow volumes.
Rest of Chapter IX.
Orientions. Rotation matrix.
Euler angles. Yaw, pitch roll.
Interpolation of orientations.
Sections XII.3, XII.3.1, XII.3.2.
Week 7
2/14 - 2/18
More Euclid angles.
Quaternions and rotation.
Mathematics development.
Sections XII.3.2, XII.3.3, XII.3.4
More quaternions.
Representation of orientations.
Sections XII.3.4, XII.3.5.
Program #4 due
Interpolation of quaternions.
Sections IV.6 (!), XII.3.7.
Week 8
2/21 - 2/25
President's Day holiday Animation.  Key framing.  Motion capture.
Articulated bodies.  Links, Joints.
Intro to Chapter XII. and
 Sections XII.4.1, XII.4.2.
Forward kinematics.
Links, 1DOF joints, Jacobian.
Sections XII.4.1-XII.4.3.
Week 9
2/28 - 3/4
Psuedo-inverse. Jacobian transpose.
Damped least squares method.
Section XII.4.3-XII.4.4.
(DLS not in as much detail as the text.)
Radiosity algorithm.  Overview.
Chapter XI. Sections XI.1.1-2.
Calculation of Form Factors.
Small patches.  Hemicube method.
Sections XI.2, XI.2.1, XI.2.2
Week 10
3/7 - 3/11
Radiosity equations with iterative methods.
Convergence proof.   Jacobi method.
XI.3.1, XI.3.2.
Gauss-Seidel and Shooting Methods.
Sections XI.3.3, XI.3,4.
Intersection testing for rays.
With sphere, with convex polytope.
Sections X.1.1, X.1.4.