# Computer aided geometric design - 4MMMG6

• #### Number of hours

• Lectures 16.5
• Projects -
• Tutorials 16.5
• Internship -
• Laboratory works -
• Written tests -

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)

Luc BIARD, 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

Prerequisites

polynomial interpolation, elementary notions of linear algebra.

Test

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.

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

• Equipment authorized :
• Equipment forbidden : all electronic devices.

• MCC en présentiel **
CC = 0.3 * TP1 + 0.3 * TP2 + 0.4 * TP3
Note Matière (session normale) = 0.5 * CC + 0.5 * E1

Note UE (session rattrapage) = 0.5 * CC + 0.5 * E2

E1 = examen session 1
E2 = examen session 2
CC=controle continue (pendant le semestre)
TP = moyenne des TP (pendant le semestre)

Documents autorisés : 2 feuilles manuscrites recto-verso

Calendar

The course exists in the following branches:

• Curriculum - Math. Modelling, Image & Simulation - Semester 7
see the course schedule for 2023-2024

Course ID : 4MMMG6
Course language(s):

The course is attached to the following structures:

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.