vectors.h File Reference

Coordinate transforms and vector arithmetics. More...

#include <math.h>
#include "qpms_types.h"
#include "qpms_error.h"

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Macros
#define	M_PI_2   (1.570796326794896619231321691639751442098584699687552910487)

Typedefs
typedef double	matrix3d[3][3]
typedef double	matrix2d[2][2]
typedef complex double	cmatrix3d[3][3]
typedef complex double	cmatrix2d[2][2]

Functions
static cart2_t	cart2_add (const cart2_t a, const cart2_t b)
	2D vector addition.
static cart2_t	cart2_substract (const cart2_t a, const cart2_t b)
	2D vector substraction.
static cart2_t	cart2_scale (const double c, const cart2_t v)
	2D vector scaling.
static double	cart2_dot (const cart2_t a, const cart2_t b)
	2D vector dot product.
static double	cart2_normsq (const cart2_t a)
static double	cart2norm (const cart2_t v)
	2D vector euclidian norm.
static pol_t	cart2pol (const cart2_t cart)
	2D cartesian to polar coordinates conversion. See Coordinate systems and default conversions.
static sph_t	pol2sph_equator (const pol_t pol)
	Polar to spherical coordinates conversion. See Coordinate systems and default conversions.
static sph_t	cart22sph (const cart2_t cart)
	2D cartesian to spherical coordinates conversion. See Coordinate systems and default conversions.
static sph_t	cart12sph_zaxis (double z)
	1D cartesian to spherical coordinates conversion. See Coordinate systems and default conversions.
static cart3_t	cart12cart3z (double z)
	1D to 3D cartesian coordinates conversion. See Coordinate systems and default conversions.
static cart3_t	cart22cart3xy (const cart2_t a)
	2D to 3D cartesian coordinates conversion. See Coordinate systems and default conversions.
static cart2_t	cart3xy2cart2 (const cart3_t a)
static double	cart3_dot (const cart3_t a, const cart3_t b)
	3D vector dot product.
static cart3_t	cart3_vectorprod (const cart3_t a, const cart3_t b)
	3D vector product a.k.a. cross product.
static double	cart3_tripleprod (const cart3_t a, const cart3_t b, const cart3_t c)
	Scalar triple product \( a \cdot ( b \times c ) \).
static double	cart3_normsq (const cart3_t a)
	3D vector euclidian norm squared.
static double	cart3norm (const cart3_t v)
	3D vector euclidian norm.
static sph_t	cart2sph (const cart3_t cart)
	3D cartesian to spherical coordinates conversion. See Coordinate systems and default conversions.
static cart3_t	sph2cart (const sph_t sph)
	Spherical to 3D cartesian coordinates conversion. See Coordinate systems and default conversions.
static cart2_t	pol2cart (const pol_t pol)
	Polar to 2D cartesian coordinates conversion. See Coordinate systems and default conversions.
static cart3_t	pol2cart3_equator (const pol_t pol)
	Polar to 3D cartesian coordinates conversion. See Coordinate systems and default conversions.
static cart3_t	cart3_add (const cart3_t a, const cart3_t b)
	3D vector addition.
static cart3_t	cart3_substract (const cart3_t a, const cart3_t b)
	3D vector substraction.
static cart3_t	cart3_scale (const double c, const cart3_t v)
	3D vector scaling
static cart3_t	cart3_divscale (const cart3_t v, const double c)
	3D vector division by scalar (N.B. argument order).
static double	cart3_dist (const cart3_t a, const cart3_t b)
	Euclidian distance between two 3D points.
static bool	cart3_isclose (const cart3_t a, const cart3_t b, double rtol, double atol)
static ccart3_t	ccart3_scale (const complex double c, const ccart3_t v)
	Complex 3D vector scaling.
static ccart3_t	ccart3_add (const ccart3_t a, const ccart3_t b)
	Complex 3D vector adition.
static ccart3_t	ccart3_substract (const ccart3_t a, const ccart3_t b)
	Complex 3D vector substraction.
static complex double	ccart3_dotnc (const ccart3_t a, const ccart3_t b)
	Complex 3D cartesian vector "dot product" without conjugation.
static ccart3_t	cart32ccart3 (cart3_t c)
	Convert cart3_t to ccart3_t.
static csphvec_t	csphvec_add (const csphvec_t a, const csphvec_t b)
	Complex 3D vector (geographic coordinates) addition.
static csphvec_t	csphvec_substract (const csphvec_t a, const csphvec_t b)
	Complex 3D vector (geographic coordinates) substraction.
static csphvec_t	csphvec_scale (complex double c, const csphvec_t v)
	Complex 3D vector (geographic coordinates) scaling.
static complex double	csphvec_dotnc (const csphvec_t a, const csphvec_t b)
	Complex 3D vector (geographic coordinates) "dot product" without conjugation.
static sph_t	sph_scale (double c, const sph_t s)
	Spherical coordinate system scaling.
static csph_t	sph_cscale (complex double c, const sph_t s)
	"Complex spherical" coordinate system scaling.
static ccart3_t	csphvec2ccart (const csphvec_t sphvec, const sph_t at)
	Coordinate transform of a vector in local geographic to global cartesian system.
static ccart3_t	csphvec2ccart_csph (const csphvec_t sphvec, const csph_t at)
	Coordinate transform of a vector in local geographic to global cartesian system. More...
static csphvec_t	ccart2csphvec (const ccart3_t cartvec, const sph_t at)
	Coordinate transform of a vector in global cartesian to local geographic system.
static csph_t	sph2csph (sph_t s)
	Convert sph_t to csph_t.
static sph_t	csph2sph (csph_t s)
	Convert csph_t to sph_t, discarding the imaginary part of radial component.
static csph_t	ccart2csph (const ccart3_t cart)
	Lossy coordinate transform of ccart3_t to csph_t. More...
static csph_t	cart2csph (const cart3_t cart)
	Real 3D cartesian to spherical (complex r) coordinates conversion. See Coordinate systems and default conversions.
static ccart3_t	csph2ccart (const csph_t sph)
	Coordinate transform of csph_t to ccart3_t.
void	print_csphvec (csphvec_t)
void	print_ccart3 (ccart3_t)
void	print_cart3 (cart3_t)
void	print_sph (sph_t)
static void	ccart3_kahaninit (ccart3_t *sum, ccart3_t *compensation)
	Kanan sum initialisation for ccart3_t.
static void	csphvec_kahaninit (csphvec_t *sum, csphvec_t *compensation)
	Kanan sum initialisation for csphvec_t.
static void	ccart3_kahanadd (ccart3_t *sum, ccart3_t *compensation, const ccart3_t input)
	Add element to Kahan sum (ccart3_t).
static void	csphvec_kahanadd (csphvec_t *sum, csphvec_t *compensation, const csphvec_t input)
	Add element to Kahan sum (csphvec_t).
static double	csphvec_norm (const csphvec_t a)
	Euclidian norm of a vector in geographic coordinates.
static double	csphvec_reldiff_abstol (const csphvec_t a, const csphvec_t b, double tolerance)
static double	csphvec_reldiff (const csphvec_t a, const csphvec_t b)
static sph_t	anycoord2sph (anycoord_point_t p, qpms_coord_system_t t)
	Conversion from anycoord_point_t to explicitly spherical coordinates. More...
static cart3_t	anycoord2cart3 (anycoord_point_t p, qpms_coord_system_t t)
	Conversion from anycoord_point_t to explicitly 3D cartesian coordinates. More...
static double	anycoord_norm (anycoord_point_t p, qpms_coord_system_t t)
	Cartesian norm of anycoord_point_t.
static pol_t	anycoord2pol (anycoord_point_t p, qpms_coord_system_t t)
	Conversion from anycoord_point_t to explicitly polar coordinates. More...
static cart2_t	anycoord2cart2 (anycoord_point_t p, qpms_coord_system_t t)
	Conversion from anycoord_point_t to explicitly 2D cartesian coordinates. More...
static double	anycoord2cart1 (anycoord_point_t p, qpms_coord_system_t t)
	Conversion from anycoord_point_t to explicitly 1D cartesian coordinates. More...
static void	qpms_array_coord_transform (void *dest, qpms_coord_system_t tdest, const void *src, qpms_coord_system_t tsrc, size_t nmemb)
	Coordinate conversion of point arrays (something to something). More...
static void	anycoord_arr2something (void *dest, qpms_coord_system_t tdest, const anycoord_point_t *src, qpms_coord_system_t tsrc, size_t nmemb)
	Coordinate conversion of point arrays (anycoord_point_t to something). More...
static void	cart3_to_double_array (double a[], cart3_t b)
	Converts cart3_t to array of doubles.
static cart3_t	cart3_from_double_array (const double a[])
	Converts array of doubles to cart3_t.
static void	cart2_to_double_array (double a[], cart2_t b)
	Converts cart2_t to array of doubles.
static cart2_t	cart2_from_double_array (const double a[])
	Converts array of doubles to cart2_t.

Variables
static const cart2_t	CART2_ZERO = {0, 0}
static const cart3_t	CART3_ZERO = {0, 0, 0}

Detailed Description

Coordinate transforms and vector arithmetics.

Function Documentation

anycoord2cart1()

static double anycoord2cart1 ( anycoord_point_t  p, qpms_coord_system_t  t  )

inlinestatic

Conversion from anycoord_point_t to explicitly 1D cartesian coordinates.

See Coordinate systems and default conversions for the conversion definitions.

anycoord2cart2()

static cart2_t anycoord2cart2 ( anycoord_point_t  p, qpms_coord_system_t  t  )

inlinestatic

Conversion from anycoord_point_t to explicitly 2D cartesian coordinates.

See Coordinate systems and default conversions for the conversion definitions.

anycoord2cart3()

static cart3_t anycoord2cart3 ( anycoord_point_t  p, qpms_coord_system_t  t  )

inlinestatic

Conversion from anycoord_point_t to explicitly 3D cartesian coordinates.

See Coordinate systems and default conversions for the conversion definitions.

anycoord2pol()

static pol_t anycoord2pol ( anycoord_point_t  p, qpms_coord_system_t  t  )

inlinestatic

Conversion from anycoord_point_t to explicitly polar coordinates.

See Coordinate systems and default conversions for the conversion definitions.

anycoord2sph()

static sph_t anycoord2sph ( anycoord_point_t  p, qpms_coord_system_t  t  )

inlinestatic

Conversion from anycoord_point_t to explicitly spherical coordinates.

See Coordinate systems and default conversions for the conversion definitions.

anycoord_arr2something()

static void anycoord_arr2something ( void *  dest, qpms_coord_system_t  tdest, const anycoord_point_t *  src, qpms_coord_system_t  tsrc, size_t  nmemb  )

inlinestatic

Coordinate conversion of point arrays (anycoord_point_t to something).

The dest and src arrays must not overlap

ccart2csph()

static csph_t ccart2csph ( const ccart3_t  cart )

inlinestatic

Lossy coordinate transform of ccart3_t to csph_t.

The angle and real part of the radial coordinate are determined from the real components of \cart . The imaginary part of the radial coordinate is then determined as the length of the imaginary part of cart projected onto the real part of cart.

N.B. this obviously makes not much sense for purely imaginary vectors (and will cause NANs). TODO handle this better, as purely imaginary vectors could make sense e.g. for evanescent waves.

csphvec2ccart_csph()

static ccart3_t csphvec2ccart_csph ( const csphvec_t  sphvec, const csph_t  at  )

inlinestatic

Coordinate transform of a vector in local geographic to global cartesian system.

Same as csphvec2ccart, but with csph_t as second argument. (The radial part (which is the only complex part of csph_t) of the second argument does not play role in the transformation, so this is completely legit

qpms_array_coord_transform()

static void qpms_array_coord_transform ( void *  dest, qpms_coord_system_t  tdest, const void *  src, qpms_coord_system_t  tsrc, size_t  nmemb  )

inlinestatic

Coordinate conversion of point arrays (something to something).

The dest and src arrays must not overlap