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.

• • G. Farin: Courbes et Surfaces pour la CGAO, Masson 1992
  • G. FARIN: Curves and Surfaces for CAGD, a practical guide, Academic Press, 1997
  • J. HOSCHEK, D. LASSER: Fundamentals of Computer Aided Geometric Design, AK Peters 1993.
  • H. Prautzsch, W. Boehm, M. Paluszny: Bezier and B-spline technique, Springer 2002.

a written examination(E) and a practical exercise(TP)

N1=2/3E1+1/3P
N2=2/3E2+1/3P