delo diplomskega seminarja
Tjaša Bajc (Author), Marjetka Krajnc (Mentor)

Abstract

V delu diplomskega seminarja bomo obravnavali interpolacijo štirih točk v ravnini s parametrično podano parabolično krivuljo. Dokazali bomo izrek, ki povezuje število interpolacijskih krivulj skozi dane točke z obliko lika, katerega oglišča so te točke, in opisali praktično konstukcijo interpolacijske krivulje na primerih. Istega problema se bomo lotili še s pomočjo kubičnih Lagrangeevih baznih polinomov, ki jim bomo s pravilno izbiro prostih parametrov znižali stopnjo in tako dobili parabolično krivuljo. Obravnavali bomo Hermitov problem, torej problem interpolacije dveh točk in tangentnih vektorjev v teh točkah s parabolično krivuljo, nazadnje pa bomo numerično izračunali red konvergence pri aproksimaciji parametrično podanih krivulj s paraboličnimi krivuljami.

Keywords

matematika;parabolične krivulje;interpolacija;Vandermondova matrika;Lagrangeevi polinomi;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [T. Bajc]
UDC: 519.6
COBISS: 18456665 Link will open in a new window
Views: 968
Downloads: 190
Average score: 0 (0 votes)
Metadata: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Other data

Secondary language: English
Secondary title: Geometric four-point parabolic interpolation
Secondary abstract: In this thesis we present the solution to four-point parabolic interpolation problem. The theorem that shows how the number of interpolation curves is related to the shape of the quadrilateral that has the given points as its vertices is proven and the construction of the interpolant in some practical examples is described. The same problem is solved again with a different approach, that is with cubic Lagrange polynomials. We find such parameters that lower the interpolant’s degree to obtain a parabolic curve. Furthermore, the Hermite’s problem is discussed, where we find a parabolic interpolant for two points and two tangent vectors. Lastly, we numerically calculate the convergence rate for approximation of parametrically given curves with parabolic curves.
Secondary keywords: mathematics;parabolic curves;interpolation;Vandermonde matrix;Lagrange polynomials;
Type (COBISS): Final seminar paper
Study programme: 0
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages: 27 str.
ID: 10961425