24 citations · 65 across the 15 of their papers we have counts for
4 papers · 1 filter
On the intrinsic geometry of polyhedra: Convex polygon coordinates
Anna B. Romanowska, Jonathan D. H. Smith, Anna Zamojska-Dzienio
There is a very extensive literature dealing with convex polytopes from the standpoints of combinatorics and numerical analysis. By contrast, the current paper adopts an alternativ…
Partitions of unity and barycentric algebras
Anna Zamojska-Dzienio
Barycentric coordinates provide solutions to the problem of expressing an element of a compact convex set as a convex combination of a finite number of extreme points of the set. T…
From affine to barycentric coordinates in polytopes
Anna B. Romanowska, Jonathan D. H. Smith, Anna Zamojska-Dzienio
Each point of a simplex is expressed as a unique convex combination of the vertices. The coefficients in the combination are the barycentric coordinates of the point. For each poin…
The inverse problem of convex polygon coordinates
A. B. Romanowska, J. D. H. Smith, A. Zamojska-Dzienio
Each convex combination of extreme points of a compact convex set represents a certain point of the convex set. Barycentric coordinates provide solutions to the inverse problem of…