Course syllabus

# Numeriska metoder för datorgrafik Numerical Methods in CAGD

## FMN100, 6 credits, A (Second Cycle)

Valid for: 2013/14
Decided by: Education Board B
Date of Decision: 2013-04-10

## General Information

Elective for: C5, D5, D5-bg, E5, E5-bg, F5, F5-bg
Language of instruction: The course will be given in English on demand

## 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 the basic algorithms and their foundations.

## Learning outcomes

Knowledge and understanding
For a passing grade the student must

be able to construct computable approximations to curves and surfaces

be able to independently implement and apply such algorithms.

Competences and skills
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

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

- be able to write a 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 the two-dimensional case.

## Examination details

Assessment: Homework reports.

Required prior knowledge: FMA420 Linear Algebra, FMAA01/05 Calculus in One Variable, FMN011/FMN050 Numerical Analysis, EDA221 Computer Graphics or equivalent.
The number of participants is limited to: No
The course overlaps following course/s: FMA135

• Farin, G: Curves and Surfaces for Cagd, A Practical Guide. Morgan Kaufmann, 2001, ISBN: 1558607374. Fifth edition.

## Contact and other information

Director of studies: Anders Holst, Studierektor@math.lth.se
Course coordinator: Carmen Arevalo, carmen@maths.lth.se
Course homepage: http://www.maths.lth.se/na/courses/FMN100