
Syllabus
The following is an approximate syllabus for the course. This is meant only
as a guideline; the topics taught on any particular day may change for
various reasons. After each class, I will update this page with what
was taught on a particular day.
 Week 1 (January 6)
 January 6:
Organizational meeting, Background material
on spaces, affine geometry.
 January 8:
Polynomials (monomials), Lagrange polynomials.
Bernstein polynomials and Bezier curves. de Casteljau's
algorithm.
 Week 2 (January 13)
 January 13:
Triangle diagrams.
Blossoming principle.
de Casteljau revisited.
 January 15:
Subdivision. Degree Raising. Functional Bezier curves.
Multilinear blossoming.
 Week 3 (January 20):
 January 20:
Curve derivatives. Curve continuity.
Cubic Hermite interpolation.
 January 22:
Change of basis via de Casteljau evaluation. Fast evaluation.
Numerics, stability of repeated linear interpolation.
 January 24:
Finish stability of repeated linear interpolation.
Triangle diagrams for interpolatory curves; Neville's algorithm.
Root finding with Bezier representation.
 Week 4 (January 27):
 January 27:
No lecture
 January 29:
Bsplines. LaneRiesenfeld.
Knot multiplicity started.
 Week 5 (February 3):
 February 3:
Knot multiplicity finished. Knot insertion.
Triangle diagrams.
LaneRiesenfeld algorithm revisited.
LaneRiesenfeld, knots in geometric progression.
 February 5:
LaneRiesenfeld algorithm extended.
Bspline Basis functions.
 Week 6 (February 10):
 February 10:
Closed Bsplines.
Degree raising Bsplines.
Degree reduction.
Direct manipulation.
 February 12:
Rational curves. Conic sections.
Generalized barycentric coordinates.
 Reading week (February 17):
 Week 7 (February 24):
 February 24:
Project overview.
Generalized Bernstein polynomials.
Triangular Bézier patches.
Blossoms.
 February 26:
Derivatives.
Storing control points: 3D and 2D arrays.
Simple Triangular Bézier patches evaluation scheme.
 Week 8 (March 2):

March 2:
Storing control points: 1D array.
Triangular Bézier patches evaluation schemes.
Evaluation of Triangular Bézier patches on a grid of points.
3:1 subdivision, 2:1 subdivision, 4:1 subdivision.
Cracking problems.
Curve evaluation,

March 4:
C0 continuity. Generalized C1 continuity.
Surfaces above the plane.
Tensorproduct patches. Derivatives, C1 continuity.
Tensorproduct Bsplines.
Surfaces above planes.
 Week 9 (March 9):
 March 9:
Evaluation methods for Tensorproduct patches.
Data interpolation: Lagrange surfaces.
Triangular data fitting  CloughTocher
 March 11:
PowellSabin.
Geometric continuity.
Crossboundary constructions. Farin's conditions.
ChiyokuraKimura. Triangular data fitting  ShirmanSequin.
 Week 10 (March 16):
 March 16:
Nielson. Boundary curves. Herron. GregoryCharrot.
 March 18:
Evaluating surface quality: line drawings, shaded images.
Evaluating surface quality: curvature plots.
More boundary curves (dBHS).
Reflection lines, isophotes.
 Week 11 (March 23):
 March 23:
Subdivision curves.
Subdivision surfaces.
 March 25:
Higher dimensional simplices.
Spatches. Apatches.
Subdivision curves.
 Week 12 (March 30):
 March 30:
Student Presentations.
Topics will include topics such as
 Degree reduction
 The Least
 Bpatches
 Spatches
 Wavelets
 Apatches
 Surface Pasting
 Implicit surfaces
