## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-70-10-M-6

## Module Identification

Module Number Module Name CP (Effort)
MAT-70-10-M-6 Spline Functions 3.0 CP (90 h)

## Basedata

CP, Effort 3.0 CP = 90 h 1 Sem. irreg. [6] Master (General) [EN] English Steidl, Gabriele, Prof. Dr. (PROF | DEPT: MAT) [MAT-SPAS] Analysis and Stochastics [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-70-10-K-6
Spline Functions
P 28 h 62 h - - PL1 3.0 irreg.
• About [MAT-70-10-K-6]: Title: "Spline Functions"; Presence-Time: 28 h; Self-Study: 62 h

## Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: irregular (by arrangement)
• Examination number: 84223 ("Spline Functions")

## Contents

• Spline functions and spline spaces,
• B-splines,
• Bézier splines (Bézier polynomials, Algorithm of de Casteljau, Bézier curves, Bézier polynomials over triangles, tensor product Bézier surfaces),
• B-spline smoothing (deBoor Algorithm).

## Competencies / intended learning achievements

Upon successful completion of this module, the students are familiar with the theory of spline functions and have become acquainted with essential algorithms based on them and used e.g. in CAGD. They understand how multivariate functions can be approximated, resp. interpolated, by spline functions and are able to apply this knowledge to various examples. They understand the proofs presented in the lecture and are able to comprehend and explain them.

## Literature

• C. de Boor: A Practical Guide to Splines,
• C. de Boor: Grundlagen der Geometrischen Datenverarbeitung,
• G. Farin: Curves and Surfaces for Computer Aided Design,
• G. Nürnberger: Approximation by Spline Functions,
• L. Schumaker: Spline Functions: Basic Theory.

## Materials

Further literature will be announced in the lecture.

None

## References to Module / Module Number [MAT-70-10-M-6]

Course of Study Section Choice/Obligation
[MAT-88.105-SG] M.Sc. Mathematics [Core Modules (non specialised)] Applied Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International [Core Modules (non specialised)] Applied Mathematics [WP] Compulsory Elective
Module-Pool Name
[MAT-GM-MPOOL-5] General Mathematics (Introductory Modules M.Sc.)