|by Jan Hakenberg||published as viXra:2002.0584 – February 29th, 2020|
Inverse Distance Weighting|
Inverse Distance Coordinates|
Figure: Basis functions of inverse distance weighting, inverse distance coordinates, and biinvariant coordinates with exponent 2 for an example set of six points in the unit square.
Abstract: We construct biinvariant generalized barycentric coordinates for scattered sets of points in any Lie group. The coordinates are invariant under left-action, right-action, and inversion, and satisfy the Lagrange property. The construction does not utilize a metric on the Lie group, unlike inverse distance coordinates. Instead, proximity is determined in a vector space of higher dimensions than the group using the Euclidean norm. The coordinates that we propose are an inverse to the unique, biinvariant weighted average in the Lie group.
|Biinvariant Generalized Barycentric Coordinates on Lie Groups||biinvariant_gen...pdf||2.5 MB|
|Biinvariant Generalized Barycentric Coordinates on Lie Groups||viXra:2002.0584||link|
|Biinvariant Generalized Barycentric Coordinates on Lie Groups||youtube||link|
Graders received some elegant solutions,
some not-so-elegant solutions,
and some so not elegant solutions.
There is light at the end of the tunnel,
but it is moving away at speed c.