(Created 2010-07-25.)
 NUMERICAL METHODS IN CAGD FMN100
Credits: 6. Grading scale: TH. Cycle: A (Second Cycle). Main field: Technology. Language of instruction: The course will be given in English on demand. Optional for: C4, D4, D4bg, E5, E5bg, F5, F5bg. Course coordinator: Carmen Arevalo, carmen@maths.lth.se and Anders Holst, ah@maths.lth.se, Numerical Analysis. Recommended prerequisits: FMA420 Linear Algebra, FMAA01/05 Calculus in One Variable, FMN011/FMN050 Numerical Analysis, EDA221 Computer Graphics or equivalent. The course might be cancelled if the number of applicants is less than 10. Assessment: Homework reports. Home page: http://www.maths.lth.se/na/courses/FMN100.

Aim
Todays CAGD software is based on efficient numerical methods to construct curves and surfaces. The goal of the course is to explain in depth basic algorithms and their foundations. The course is an important link between numerical analysis and informatics education.

Knowledge and understanding
For a passing grade the student must

be able to construct computable approximations to curves and surfaces. Moreover, students must be able to independently implement and apply such algorithms.

Skills and abilities
For a passing grade the student must

- be able to independently select and apply computational algorithms

- be able to evaluate both accuracy and relevance of numerical results.

Judgement and approach
For a passing grade the student must

- write a logically well structured report, using suitable terminology, on the construction of basic numerical methods and algorithms.

- write an algorithmically well structured report, using suitable terminology, on the numerical approximation of curves and surfaces.

Contents
Polynomial and spline interpolation, Bézier curves, de Casteljau's algorithm, blossoms, de Boor's algorithm and de Boor points, control polygons, NURBS, different parametrizations of curves, surfaces and extensions to 2D.

Literature
Farin, G: Curves and Surfaces for Computer Aided Geometric Design, ISBN 0122490541, Academic Press, 1996.
The literature may be changed.