CANISIUS lecture -- Jorg Peters
Mathematics of Computer Graphics

What gives Pixar's characters their looks? How does one simulate a flock of birds? The course participants will discover the power and beauty of affine invariant representations of geometry based on barycentric coordinates, the use of control structures and curved geometry via refinement.
To make the experience concrete course participants will build a 2D drawing environment using a mathematical toolkit and see programs for graphical interaction with geometry using OpenGL, the lingua franca of graphic programming.

An important aspect is for the participants to understand how the practical and theoretical tools generalize to representing geometry and functions in higher dimensions. Creating and modifying shapes to meet a given functionality (shape, smoothness, interpolation) is central to web-age activities stretching from animation to scientific computing.

Topic	Homework
Introduction (Adobe Acrobat PDF) Four views of Bezier curves Properties of the Bezier form in one variable (Adobe Acrobat PDF)	Draw the example curves Why do the Bezier basis functions sum to 1?
Properties of Bezier forms Bezier patches (Adobe Acrobat PDF, 3 Mb) Multivariate Bezier forms	Draw example surfaces Do some of the exercises in the Bezier handout
some test problems (Adobe Acrobat PDF) Matlab session implementation (in Matlab)	Hand in problems 3 and 5 of "some test problems" on Friday for your grade
more test problems (Adobe Acrobat PDF) uniform splines uniform spline curves implemented	Draw B-spline curves
Box splines (Adobe Acrobat PDF) B-splines Subdivision Curves and Surfaces	3pm Public Lecture Draw the example Box spline Draw subdivision curves

Gerald Farin: Curves and Surfaces for CAGD, 5th edition Morgan Kaufmann Publishers, ISBN = "1-55860-737-4"
Prautzsch, Boehm, Paluszny: Bezier and B-spline Techniques, Springer 3-540-43761-4