Baricentrične koordinate : delo diplomskega seminarja

Murnik, Petja (author), Jaklič, Gašper (mentor)

V diplomskem delu obravnavam baricentrične koordinate, s katerimi lahko zapišemo točke v trikotniku v ravnini ali v kakšnem drugem d-simpleksu. Zatem uvedem posplošene baricentrične koordinate, ki jih delimo med homogene ter računske koordinate. Predstavim nekaj primerov obeh ter jih med seboj primerjam. Zaključim s predstavitvijo dveh primerov uporabe posplošenih baricentričnih koordinat, to sta interpolacija ter baricentrična preslikava.

• Language: Slovenian
• Keywords: težišče, baricentrične koordinate, posplošene baricentrične koordinate, interpolacija, baricentrična preslikava
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2023
• PID: 20.500.12556/RUL-150445
• UDC: 519.6
• COBISS.SI-ID: 164779267
• Publication date in RUL: 17.09.2023

Secondary language

• Language: English
• Title: Barycentric Coordinates

Abstract

In my thesis, I address barycentric coordinates, which can be used to express points in a triangle in the plane or in any other d-simplex. Subsequently, I introduce generalized barycentric coordinates, which we divide into homogeneous and computational coordinates. I present some examples of both and compare them. I conclude by presenting two examples of the use of generalized barycentric coordinates, namely interpolation and barycentric mapping.

• Keywords: barycenter, barycentric coordinates, generalized barycentric coordinates, interpolation, barycentric mapping