- Spline functions and spline spaces,
- Bézier splines (Bézier polynomials, Algorithm of de Casteljau, Bézier curves, Bézier polynomials over triangles, tensor product Bézier surfaces),
- B-spline smoothing (deBoor Algorithm).
Spline Functions (M, 3.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-70-10-M-6||Spline Functions||3.0 CP (90 h)|
|CP, Effort||3.0 CP = 90 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (General)|
|Area of study||[MAT-SPAS] Analysis and Stochastics|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
|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")
Evaluation of grades
The grade of the module examination is also the module grade.
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.
- 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.
Further literature will be announced in the lecture.
Requirements for attendance of the module (informal)
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-14-11-M-3] Introduction to Numerical Methods (M, 9.0 LP)
Requirements for attendance of the module (formal)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|
|[MAT-GM-MPOOL-5]||General Mathematics (Introductory Modules M.Sc.)|