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Behaviour of exponential three-point coordinates at the vertices of convex polygons

Anisimov, Dmitry ; Hormann , Kai ; Schneider

In: Journal of computational and applied mathematics, 2019, vol. 350, p. 114-129

Barycentric coordinates provide a convenient way to represent a point inside a triangle as a convex combination of the triangle’s vertices and to linearly interpolate data given at these vertices. Due to their favourable properties, they are commonly applied in geometric modelling, finite element methods, computer graphics, and many other fields. In some of these applications, it is desirable...

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Analysis and new constructions of generalized barycentric coordinates in 2D

Anisimov, Dmitry ; Hormann, Kai (Dir.)

Thèse de doctorat : Università della Svizzera italiana, 2017 ; 2017INFO004.

Different coordinate systems allow to uniquely determine the position of a geometric element in space. In this dissertation, we consider a coordinate system that lets us determine the position of a two-dimensional point in the plane with respect to an arbitrary simple polygon. Coordinates of this system are called generalized barycentric coordinates in 2D and are widely used in computer...

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