According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review. The evaluation of outcome prior learning is made as a continuous training during the semester. Linear algebra, resolution of linear systems, use of matlab or python.
Build a B-Spline curve of n given points (analytically and by a subdivision algorithm (de Casteljau, de Boor))Īpprehend, modify a NURBS curve. Determine and compute the interpolating spline, the smoothing spline, and the least squares spline of n given points. Determine the most efficient method to solve a least squares problem by identifying the characteristics of the problem. The extension to NURBS curves and to surface modelling in CAD. A (the MATLAB command null(A) provides us with an orthonormal basis of Null(A)), while (uk)m. Piecewise functions, C k continuity, natural cubic splines and their local and global representations, basis of B-Splines, B-Spline curves and their control points. Application to the least squares problem. In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree. QR factorization: the Gram-Schmidt and Householder methods To go from discrete data to continuous functions.Īt the end of this module, the student will have understood and be able to explain (main concepts): This module is organized in course, tutorials and labworks. B-Splines, B-Spline curves, NURBS, NURBS curves, introduction to subdivision (de Casteljau’s algorithm, de Boor’s algorithm) By cubic natural spline functions (interpolation, smoothing, and least squares). Singular value decompositions and some properties: link with the euclidian norm and the approximation with a weak rank matrix. QR factorization thanks to the Gram-Schmidt and Householder method.
Matrix computation for the least squares method: Two MATLAB codes of very similar architecture were developed on a standard PC Pentium IV as follows: (i) a code based on rectangular 4-node (32-DOF) Hermite elements (ii) a code based on contemporary cubic B-splines in conjunction with double inner knots the basis functions and their derivatives were created using the spcol function.