ylm::Tags::Tangents< Frame > Struct Template Reference

Tangents(i,j) is $\partial x_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}}^i/\partial q^j$, where $x_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}}^i$ are the Cartesian coordinates of the surface (i.e. CartesianCoords) and are considered functions of $(\theta ,\varphi )$. 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 $\partial x_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}}^i/\partial q^j$, where $x_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}}^i$ are the Cartesian coordinates of the surface (i.e. CartesianCoords) and are considered functions of $(\theta ,\varphi )$.

$\partial /\partial q^0$ means $\partial /\partial \theta$; and $\partial /\partial q^1$ means $\csc \theta \partial /\partial \varphi$. Note that the vectors Tangents(i,0) and Tangents(i,1) are orthogonal to the NormalOneForm $s_i$, i.e. $s_i\partial x_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}}^i/\partial q^j=0$; 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.

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

• src/NumericalAlgorithms/SphericalHarmonics/Tags.hpp