Tangents(i,j) is \(\partial x_{\rm surf}^i/\partial q^j\), where \(x_{\rm surf}^i\) are the Cartesian coordinates of the surface (i.e. CartesianCoords) and are considered functions of \((\theta,\phi)\). More...

#include <Tags.hpp>

Public Types
using	type = aliases::Jacobian< Frame >

Detailed Description

template<typename Frame>
struct ylm::Tags::Tangents< Frame >

Tangents(i,j) is \(\partial x_{\rm surf}^i/\partial q^j\), where \(x_{\rm surf}^i\) are the Cartesian coordinates of the surface (i.e. CartesianCoords) and are considered functions of \((\theta,\phi)\).

\(\partial/\partial q^0\) means \(\partial/\partial\theta\); and \(\partial/\partial q^1\) means \(\csc\theta\,\,\partial/\partial\phi\). Note that the vectors Tangents(i,0) and Tangents(i,1) are orthogonal to the NormalOneForm \(s_i\), i.e. \(s_i \partial x_{\rm surf}^i/\partial q^j = 0\); this statement is independent of a metric. Also, Tangents(i,0) and Tangents(i,1) are not necessarily orthogonal to each other, since orthogonality between 2 vectors (as opposed to a vector and a one-form) is metric-dependent.

The documentation for this struct was generated from the following file:

src/NumericalAlgorithms/SphericalHarmonics/Tags.hpp

Public Types

Detailed Description