Martix computation and geometry

Objectifs

Objectives:
At the end of this module, the student will have understood and be able to explain (main concepts):
- QR factorization: the Gram-Schmidt and Householder methods
- Singular value decomposition
- Application to the least squares problem.
- Piecewise functions, Ck continuity, natural cubic splines and their local and global representations, basis of B-Splines, B-Spline curves and their control points.
- The extension to NURBS curves and to surface modelling in CAD.

The student will be able to:
- Determine the most efficient method to solve a least squares problem by identifying the characteristics of the problem.
- Determine and compute the interpolating spline, the smoothing spline, and the least squares spline of n given points.
- Build a B-Spline curve of n given points (analytically and by a subdivision algorithm (de Casteljau, de Boor))
- Apprehend, modify a NURBS curve.

Pré-requis

Necessary knowledge:

Linear algebra, resolution of linear systems, use of matlab or python.

Évaluation

L’évaluation des acquis d’apprentissage est réalisée en continu tout le long du semestre. En fonction des enseignements, elle peut prendre différentes formes : examen écrit, oral, compte-rendu, rapport écrit, évaluation par les pairs…