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 - 1/7Hermite polynomials.
Piecewise Bezier curves.
Sections VII.4 & 5. Review VII.1C1- 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 - 1/14DeCasteljau 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 - 1/21Martin Luther King
holiday
Circular Bezier curve.
Conic sections.
Surface of Revolution.
Sections VII.13, VII.14.
Program #1 dueCircular Disks with
Bezier patches
Variation diminishing property.
Other properties. B-Splines overview.
Week 4
1/24 - 1/28Raytracing 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 dueAdvanced ray tracing.
Section IX.2.
Week 5
1/31 - 2/4Advanced ray tracing,
cont'd.
Section IX.2RayTrace software. (Appendix
B)
Tricks to avoid ray tracing.
Project #3 (3DS) dueNo class
Week 6
2/7 - 2/11Sampling 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.Midterm
Week 7
2/14 - 2/18More Euclid angles.
Quaternions and rotation.
Mathematics development.
Sections XII.3.2, XII.3.3, XII.3.4More quaternions.
Representation of orientations.
Sections XII.3.4, XII.3.5.
Program #4 dueInterpolation of
quaternions.
Slerping.
Sections IV.6 (!), XII.3.7.
Week 8
2/21 - 2/25President'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 - 3/4Psuedo-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 - 3/11Radiosity equations with
iterative methods.
Convergence proof. Jacobi method.
XI.3.1, XI.3.2.Gauss-Seidel and Shooting
Methods.
Overrelaxation.
Sections XI.3.3, XI.3,4.Intersection testing for
rays.
With sphere, with convex polytope.
Sections X.1.1, X.1.4.