Geometric Modeling 1

# Basics

# Polynomials

- Bases
- Mononomials
- Lagrange polynomials
- Newton polynomials (equidistant, arbitrary)
- Bernstein polynomials
- Cubic Hermite Splines
- Cheybychev polynomials of the first kind

- Evaluation
- Mononomial
- Lagrange/Aitken-Neville
- Newton (equidistant only)
- Bernstein/de Casteljau

- Interpolation
- Problem description
- Polynomial interpolation
- Mononomial interpolation
- Lagrange interpolation
- Newton interpolation (equidistant only)
- Cheybychev interpolation

- Choice of parameter values
- Globally best approximation
- Locally best approximation

- Approximation
- Problem description
- Least-Squares approximation
- Heuristic parameter estimation
- Approximation error

# Bézier Curves

- Representation
- Degree elevation
- Blossoms
- Subdivision
- Variation diminishing property
- Piecewise polynomials

# B-Splines

page revision: 5, last edited: 29 Mar 2007 09:03