Math 155B - Introduction to Computer Graphics - Winter 2004

Midterm topics.

Topics: Some questions may ask for calculations, others may just be conceptual.

 Bezier Curves and Surfaces B spline curves Degree 1,2,3 Bezier curves Higher degree Bezier curves. De Castaljau algorithm Derivatives Subdivision Piecewise Bezier Curves C1 and G1 continuity.  Sufficient and necessary conditions. Degree elevation. Bezier patches Rational curves, Conic sections, Circles. Surface of revolution. Catmull-Rom and Overhauser curves. Uniform and non-uniform B-splines and Blending functions Bezier curves as B-splines and B-splines as piecewise Bezier curves. Properties, including Ci continuity and repeated knots. de Boor Algorithm Derivatives Knot insertion Degree elevation NURBS, Conic sections, Circles. Interpolating with degree 3 curves.

Not covered:   TCB curves (Tension, Continuity, Bias); Interpolating Bezier surfaces, Blossoms.

Formulas on a to-be-supplied cheat sheet.
Bezier curve degree elevation, page 172.
Cox-de Boor, page 206
De Boor Algorithm Formulas, VIII.8 and VIII.9, page 214.
Derivatives of B-splines, VIII.18, page 231.
Knot insertion formulas.   VIII.27 and the preceeding one for u-hat. Page 224.