magistrsko delo
Sabina Kramer (Author), Emil Žagar (Mentor)

Abstract

Na začetku bomo definirali osnovne lastnosti ravninskih parametričnih krivulj, kot so tangenta, ukrivuljenost, normala in paralelna krivulja. Potem se bomo posvetili polinomom v Bernsteinovi bazi. Na podlagi teh polinomov bomo definirali Bézierjeve krivulje in predstavili pomen kontrolnega poligona. Sledila bo interpolacija s kubičnimi Bézierjevimi krivuljami. Definirali bomo krivulje s pitagorejskim hodografom (PH krivulje). Opisali bomo njihove glavne lastnosti in predstavili formule za izračun kontrolnih točk. Nato se bomo ukvarjali z interpolacijo s PH krivuljami stopnje 5. Predstavili bomo kriterij za izbiro najboljše rešitve in konstruirali zlepke, ki jih bomo primerjali s kubičnimi zlepki. Konstruirali bomo paralelne krivulje in predstavili metodo za obrezovanje teh krivulj.

Keywords

parametrična krivulja;tangentni vektor;ukrivljenost;paralelna krivulja;Berensteinova baza;Bézierjeva krivulja;pitagorejski hodograf;PH krivulja;Hermiteova interpolacija;zlepki;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UL FMF - Faculty of Mathematics and Physics
Publisher: [S. Kramer]
UDC: 519.6
COBISS: 18459225 Link will open in a new window
Views: 782
Downloads: 301
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Other data

Secondary language: English
Secondary title: Pythagorean-Hodograph curves and interpolation
Secondary abstract: We will define basic parametric planar curve properties, like tangent vector, curvature, normal vector and offset. Then, we will describe polynomials in the Bernstein basis and use that concept for defining Bézier curves and control polygon. Interpolation with cubic Bézier will follow. We will define pythagorean-hodograph (PH) curves, describe their main properties and calculate control points. We will interpolate given data with the PH quintics and show a criteria for choosing the best solution. We will construct PH quintic splines and compare them to the ordinary cubic splines. We will finish with constructing offset curves and describe trimming procedure.
Secondary keywords: parametric curve;tangent vector;curvature;offset curve;Bernstein basis;Bézier curve;pythagorean hodograph;PH curve;Hermite interpolation;spline;
Type (COBISS): Master's thesis/paper
Study programme: 0
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 2. stopnja
Pages: IX, 51 str.
ID: 10962507