Konstrukcija ravninskih in prostorskih krivulj B-zlepkov s Pitagorejskim hodografom

magistrsko delo

Brina Ribič (Author), Marjetka Krajnc (Mentor)

Abstract

Krivulje s pitagorejskim hodografom so poseben razred parametrično podanih krivulj, pri katerih je ena izmed ključnih lastnosti eksakten izračun ločne dolžine krivulje brez uporabe numeričnih orodij. Parametrično podane krivulje predstavimo v bazi B-zlepkov, kar omogoča učinkovito konstrukcijo krivulj s pitagorejskim hodografom ter zagotavlja lokalno kontrolo oblike, zveznost in numerično stabilnost. V namen izvajanja ustreznih operacij nad krivuljami, ravninske parametrično podane krivulje s pitagorejskim hodografom predstavimo z uporabo kompleksnih števil, prostorske pa s pomočjo kvaternionov. Krivulje s pitagorejskim hodografom konstruiramo iz tako imenovanih praslik - poljubnih parametrično podanih krivulj, ki jih z ustrezno operacijo nad kompleksnimi števili oziroma kvaternioni pretvorimo v hodografe krivulj s pitagorejskim hodografom. Dobljeni hodograf še integriramo in dobimo končno krivuljo s pitagorejskim hodografom.

Keywords

krivulje s pitagorejskim hodografom;kompleksna števila;kvaternioni;B-zlepki;

Data

Language:	Slovenian
Year of publishing:	2025
Typology:	2.09 - Master's Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[B. Ribič]
UDC:	519.6
COBISS:	239162115
Views:	132
Downloads:	47
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Construction of planar and spatial Pythagorean-Hodograph B-spline curves
Secondary abstract:	Pythagorean-Hodograph curves are a special class of parametrically given curves, whose key property is the exact calculation of the arc length of the curve, i.e. without using numerical tools. Parametrically given curves are represented in a B-spline basis, which allows efficient construction of Pythagorean-Hodograph curves and provides local shape control, continuity and numerical stability. In order to perform appropriate operations on curves, planar parametric curves are represented with complex valued functions, while spatial curves are represented using quaternions. Pythagorean-Hodograph curves are constructed from so-called preimage, arbitrary parametric curve, which is transformed into a hodograph of the Pythagorean-Hodograph curve using appropriate operation over complex or quaternion valued functions. The resulting hodograph is further integrated to obtain the final Pythagorean-Hodograph curve.
Secondary keywords:	Pythagorean-Hodograph curves;complex numbers;quaternions;B-splines;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 2. stopnja
Pages:	VIII, 53 str.
ID:	26719635