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Number of hours
Lectures : 16.5
Tutorials : 16.5
Laboratory works : -
Projects : -
Internship : -
Written tests : -
ECTS : 3.0
Officials :Stefanie HAHMANN
Spline curves and surfaces are the standard mathematical models in CAD/CAM systems like CATIA or EUKLID. Further application areas are medical imaging, computer graphics and virtual reality, scientific computing or geographical information systems. This course presents the different base models and the main algorithms.
(1) CURVES IN GEOMETRIC DESIGN :
Bézier curves : Bernstein polynomials, DeCastejau algorithm and its applications, geometric properties.
B-spline functions :the B-spline basis, multiplicity of knots, order of continuity, local support.
B-spline curves : parametric B-splines, control polygon, DeBoor algorithm, knot insertion. (2) SURFACES IN GEOMETRIC DESIGN : tensor product and triangular Bézier patches, algorithms. (3) SPLINE INTERPOLATION and APPROXIMATION: spline spaces, interpolation by polynomial spline, minimization of energy, Least squares approximation, introduction of weights and constraints. Spline approximation, algorithms
polynomial interpolation, elementary notions of linear algebra.
SESSION NORMALE : a written examination(E1) and a practical exercise(P) Duration : 2h Documents authorized : all handwritten documents, dictionary. Documents forbidden : books, photocopies of books. Equipment
Equipment authorized :
Equipment forbidden : all electronic material. Comments :
SESSION DE RATTRAPAGE : a written examination or an oral examination if number of students < 5 (E2) Duration : 2h Documents authorized : all handwritten documents, dictionary. Documents forbidden : books, photocopies of books. Equipment