interpolate sampled spherical data linearly over a triangulation.

Syntax

f = S2FunTri(directions, values)
f = S2FunTri(triangulation, values)
f = S2FunTri(lambda v: v.z**2)

Description

The value within a spherical triangle is the barycentric interpolation of its three vertex values. Duplicate directions are merged and their values averaged. Passing a callable samples it on a grid of 1.5 degrees before constructing the triangulation. The result can be evaluated with f(queryDirections).

This representation stores sample values rather than harmonic coefficients. Products, powers and pointwise transforms operate at the vertices and interpolate the transformed values between them. They can differ from applying the same transform after interpolation.

Input

`nodes`	vector3d directions, S2Triangulation, or a vectorised callable of directions
`values`	one row of sampled values per node; several columns represent several functions

Output

f S2FunTri

Properties

`vertices`	unit directions of the triangulation
`values`	numeric array with one row per vertex and one column per function
`tri`	S2Triangulation defining the face connectivity
`frame`	reference frame carried by the vertices

Members

abs	the absolute value of the function, taken at the vertices, again a function on the triangulation
CS	the frame of the vertices, MATLAB’s sF.CS
eval	the values at the directions v, the barycentric mean of the values at the corners of the triangle each lies in
frame	the frame of the vertices
mean	estimate the spherical mean using Voronoi areas around the sample vertices
min	the minimum of a function on SO(3) or the sphere, the value and the position, numLocal local minima
plot	plot(x, …) draws x as its kind is drawn
plus
power
rdivide
rotate	rotate(x, rot) is x.rotate(rot), or rot * x for an object without that method
S2FunTri	interpolate sampled spherical data linearly over a triangulation
sqrt	take square roots at the vertices and interpolate those values linearly
textureIndex	the texture index of a function on SO(3) or on the sphere, the squared L2 norm of its harmonic expansion
times
uminus
vertices	the vertices of the triangulation, the directions the values are given at
volume	the share of orientations within a radius of a centre: the integral of f over the ball, int_{angle(g, c) < r} f(g) dg, relative to the integral over all orientations

MATLAB’s S2FunTri_index

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/S2FunTri_index_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.

The class S2FunTri