Syllabus academic year 2007/2008
 NUMERICAL METHODS IN CAGD FMN100

Higher education credits: 6. Grading scale: TH. Level: A (Second level). Language of instruction: The course will be given in English on demand. Optional for: C4, C4bg, D4, D4bg, E4bg, F4, F4tmb, F4tvb, L4. Course coordinator: Carmen Arevalo, carmen@maths.lth.se, Numerisk analys. Recommended prerequisits: Calculus, Linear Algebra, Differential equations. The course might be cancelled if the numer 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 foundation. 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 have to implement and to apply such algorithms independently.

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 in suitable terminology on the construction of basic mathematical models and algorithms.

- write a algorithmically well structured report in 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.