C-krivulje

magistrsko delo

Mateja Čarman (Author), Emil Žagar (Mentor)

Abstract

C-Bézierjeve krivulje predstavljajo razširitev kubičnih Bézierjevih krivulj. Definirane so kot linearna kombinacija baznih funkcij $\sin t$, $\cos t$ in 1. V definiciji nastopa še parameter $\alpha$, ki dodatno vpliva na obliko krivulje. C-Bézierjeve krivulje v limitnem primeru $\alpha \to 0$ konvergirajo h kubičnim Bézierjevim krivuljam. Obe družini krivulj se zaradi številnih lepih geometrijskih lastnosti uporabljata v računalniško podprtem geometrijskem oblikovanju. V delu na kratko predstavimo še sorodne Fergusonove krivulje in njihovo razširitev na C-krivulje. Glavna prednost C-Bézierjevih krivulj je ta, da lahko z njimi eksaktno narišemo krožni lok in lok elipse. V delu je podana geometrijska karakterizacija krivulje, ki predstavlja krožni lok in polovico loka elipse. Na koncu predstavimo še Bézierjeve in C-Bézierjeve krivulje kot PH krivulje, ki se uporabljajo v programih CNC strojev.

Keywords

matematika;gladkost;interpolacija s krivuljami;algoritmi za aproksimacijo funkcij;računalniško podprto oblikovanje;

Data

Language:	Slovenian
Year of publishing:	2019
Typology:	2.09 - Master's Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[M. Čarman]
UDC:	519.6
COBISS:	18656089
Views:	1714
Downloads:	219
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	C-curves
Secondary abstract:	The C-Bézier curves represent the extension of the cubic Bézier curves. They are defined as a linear combination of the basis functions $\sin t$, $\cos t$ and 1. The definition also includes a parameter $\alpha$ that additionally affects the shape of the curve. In the limit case $\alpha \to 0$, the C-Bézier curves converge to Cubic Béziers curves. Both families of curves are used in computer aided geometric design because of their numerous beautiful geometric properties. In this work we briefly present the related Ferguson curves and their extension to the C-curves. The main advantage of the C-Bézier curves is that we can accurately plot the circular arc and arc ellipse. The geometric characterization of the curve, which represents a circular arc and a half of the arc of the ellipse, is also given in the paper. Finally, we present Bézier and C-Bézier curves as PH curves used in CNC machines.
Secondary keywords:	mathematics;smoothing;curve fitting;algorithms for functional approximation;computer aided design;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Pedagoška matematika
Pages:	IX, 63 str.
ID:	11161936