/**
* \brief
* Compute the curl of B and it's parallel and perpendicular components at a given point.
*
* \details
* Computes \f$ \nabla\times B \f$, \f$ (\nabla\times B)_\parallel \f$, and \f$ (\nabla\times B)_\perp \f$.
*
*
* \param[in] u0 Position (in GSM) to use.
* \param[out] CurlB The computed curl of B at position u0.
* \param[out] CurlB_para The computed parallel component of curl of B at position u0.
* \param[out] CurlB_perp The computed perpendicular component of curl of B at position u0.
* \param[in] DerivScheme Derivative scheme to use (can be one of LGM_DERIV_SIX_POINT, LGM_DERIV_FOUR_POINT, or LGM_DERIV_TWO_POINT).
* \param[in] h The delta (in Re) to use for grid spacing in the derivative scheme.
* \param[in,out] m A properly initialized and configured Lgm_MagModelInfo structure.
*
*
* \author Mike Henderson
* \date 2011
*
*/
void Lgm_CurlB2( Lgm_Vector *u0, Lgm_Vector *CurlB, Lgm_Vector *CurlB_para, Lgm_Vector *CurlB_perp, int DerivScheme, double h, Lgm_MagModelInfo *m ) {
double g;
Lgm_Vector Bvec;
Lgm_CurlB( u0, CurlB, DerivScheme, h, m );
m->Bfield( u0, &Bvec, m );
Lgm_NormalizeVector( &Bvec );
// Compute parallel component of CurlB
g = Lgm_DotProduct( &Bvec, CurlB );
*CurlB_para = *CurlB;
Lgm_ScaleVector( CurlB_para, g );
// Compute perpendicular component of CurlB (CurlB_perp = CurlB - CurlB_para)
Lgm_VecSub( CurlB_perp, CurlB, CurlB_para );
return;
}
/**
* \brief
* Compute the gradient of B and it's parallel and perpendicular components at a given point.
*
* \details
* Computes \f$ \nabla B \f$, \f$ (\nabla B)_\parallel \f$, and \f$ (\nabla B)_\perp \f$.
*
*
* \param[in] u0 Position (in GSM) to use.
* \param[out] GradB The computed curl of B at position u0.
* \param[out] GradB_para The computed parallel component of curl of B at position u0.
* \param[out] GradB_perp The computed perpendicular component of curl of B at position u0.
* \param[in] DerivScheme Derivative scheme to use (can be one of LGM_DERIV_SIX_POINT, LGM_DERIV_FOUR_POINT, or LGM_DERIV_TWO_POINT).
* \param[in] h The delta (in Re) to use for grid spacing in the derivative scheme.
* \param[in,out] m A properly initialized and configured Lgm_MagModelInfo structure.
*
*
* \author Mike Henderson
* \date 2011
*
*/
void Lgm_GradB2( Lgm_Vector *u0, Lgm_Vector *GradB, Lgm_Vector *GradB_para, Lgm_Vector *GradB_perp, int DerivScheme, double h, Lgm_MagModelInfo *m ) {
double g;
Lgm_Vector Bvec;
Lgm_GradB( u0, GradB, DerivScheme, h, m );
m->Bfield( u0, &Bvec, m );
Lgm_NormalizeVector( &Bvec );
// Compute parallel component of GradB
g = Lgm_DotProduct( &Bvec, GradB );
*GradB_para = *GradB;
Lgm_ScaleVector( GradB_para, g );
// Compute perpendicular component of GradB (GradB_perp = GradB - GradB_para)
Lgm_VecSub( GradB_perp, GradB, GradB_para );
return;
}
/*
* Given vectors a and b, compute the angle between them in degrees
*/
double Lgm_VectorAngle(Lgm_Vector *a, Lgm_Vector *b) {
double ang;
Lgm_Vector u, v;
u = *a;
v = *b;
Lgm_NormalizeVector(&u);
Lgm_NormalizeVector(&v);
ang = acos(Lgm_DotProduct(&u, &v));
return (ang*DegPerRad);
}
/**
* \brief
* Initialize a Lgm_SlerpInfo structure.
* \details
* This routine computes \f$\sin(\phi)\f$, \f$\cos(\phi)\f$, and
* \f$\phi\f$. Where \f$\phi\f$ is the angle between the initial and final
* unit vectors. This is done outside the main slerp routine because you
* may want to perform many interps with the same endpoint vectors.
*
* \param[in] a: initial unit vector.
* \param[in] b: final unit vector.
*
* \param[in,out] si: Lgm_SlerpInfo structure.
*
*/
void Lgm_InitSlerp( Lgm_Vector *a, Lgm_Vector *b, Lgm_SlerpInfo *si ) {
Lgm_Vector v, w;
si->CosPhi = Lgm_DotProduct( a, b );
w = *a; Lgm_ScaleVector( &w, si->CosPhi ); // w = cos(phi)*a-hat
Lgm_VecSub( &v, b, &w ); // v = b-hat - cos(phi)*a-hat
si->SinPhi = Lgm_Magnitude( &v ); // sin(phi)
si->Phi = atan2( si->SinPhi, si->CosPhi ); // Phi
}
