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.