Number of hours
- Lectures 16.5
- Projects -
- Tutorials 16.5
- Internship -
- Laboratory works -
- Written tests -
ECTS
ECTS 3.0
Goal(s)
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.
Responsible(s)
Stefanie HAHMANN
Content(s)
(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.
Test
Evaluation : 34% of Projet (évaluation en continu et sur le rendu) + soutenance and 66% of Examen Ecrit (2h)
Resit : 34% of Projet (évaluation en continu et sur le rendu) + soutenance (reported score) and 66% of Examen Ecrit (2h)
CONTRÔLE CONTINU = CC
Type d'évaluation : 1 project on computer + project presentation
SESSION NORMALE :
a written examination (E1)
Duration : 2h
Documents authorized : one double-sided handwritten sheet of A4 paper
Documents forbidden : books, photocopies of books.
Equipment
- Equipment authorized : nothing
- Equipment forbidden : all electronic material.
COMMENTS : Commentaires :
Note UE (session normale) = (CC +2 * E1)
SESSION DE RATTRAPAGE (catch-up):
a written examination (E2)
Duration : 2h
Documents authorized : one double-sided handwritten sheet of A4 paper
Documents forbidden : books, photocopies of books.
Equipment
- Equipment authorized : nothing
- Equipment forbidden : all electronic devices.
COMMENTS:
Note UE (catch-up session) = (CC + 2 * E2)
Calendar
The course exists in the following branches:
- Curriculum - Math. Modelling, Image & Simulation - Semester 7
Additional Information
Course ID : 4MMMG6
Course language(s): 
The course is attached to the following structures:
- Team Image Vision Interaction Multimedia Bioinfo
You can find this course among all other courses.
Bibliography
- 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.