Description

Functions for analytic coordinate transformations.

This module provides some common coordinate transformations in terms of the direct mapping, inverse mapping and jacobian. All of these should be implement following similar naming conventions.

Affine transformation (logical mesh is [0,1]x[0,1]):

\[ x1 = (b1-a1)*(cos(alpha)*eta1-sin(alpha)*eta2) + a1 \]

\[ x2 = (b2-a2)*(sin(alpha)*eta1+cos(alpha)*eta2) + a2 \]

developer's note: made the choice of the params array as the full sequence (A1 B1 A2 B2) as the same params array may thus be passed as argument any call related with this transformation. Delete these formerly default values:

A1 = -1.0
B1 = 1.0
A2 = -1.0
B2 = 1.0

Homography transformation (logical mesh is [0,1]x[0,1]):

the homography is used to rectify a perspective image, for example to generate a "plan" view of a building from a "perspective" photo. We can also convert a square to a trapeze.

\[ x1 = (a*eta1*b*eta2+c)/(g*eta1+h*eta2+1) \]

\[ x2 = (d*eta1*e*eta2+f)/(g*eta1+h*eta2+1) \]

a = fixed scale factor in x1 direction with scale x2 unchanged.
b = scale factor in x1 direction proportional to x2 distance from origin.
c = origin translation in x1 direction.
d = scale factor in x2 direction proportional to x1 distance from origin.
e = fixed scale factor in x2 direction with scale x1 unchanged.
f = origin translation in x2 direction.
g = proportional scale factors x1 and x2 in function of x1.
h = proportional scale factors x1 and x2 in function of x2.

Rubber_sheeting transformation

the rubber-sheeting is similar to homography. The difference is that the Homography gives priority to alignments, whereas the Rubber-Sheeting gives priority to linear proportions.

\[ x1 = a*eta1*eta2+b*eta1+c*eta2+d \]

\[ x2 = e*eta1*eta2+f*eta1+g*eta2+h \]

a = scale factor in x1 direction proportional to the multiplication x1 * x2.
b = fixed scale factor in x1 direction with scale x2 unchanged.
c = scale factor in x1 direction proportional to x2 distance from origin.
d = origin translation in x1 direction.
e = scale factor in x2 direction proportional to the multiplication x1 * x2.
f = fixed scale factor in x2 direction with scale x1 unchanged.
g = scale factor in x2 direction proportional to x1 distance from origin.
h = origin translation in x2 direction.

Polar coordinate transformation (r = eta1, theta = eta2):

\[ x1 = eta1 * cos (eta2) \]

\[ x2 = eta1 * sin (eta2) \]

Alternative formulation for the polar coordinate transformation:

\[ X1 = (Rmin + (Rmax-Rmin)*eta1)*cos(2*pi*eta2) \]

\[ X2 = (Rmin + (Rmax-Rmin)*eta1)*sin(2*pi*eta2) \]

Where eta1 and eta2 are defined in the interval [0,1]. The 'params' array contains the information (R1, R2). Typically:

R1 = 0.1, R2 = 1.0

"Colella transformation"; sinusoidal product (see P. Colella et al. JCP 230 (2011) formula (102) p 2968):

\[ x1 = eta1 + alpha1 * sin(2*\pi/L1 * eta1) * sin(2*\pi/L2 * eta2) \]

\[ x2 = eta2 + alpha2 * sin(2*\pi/L1 * eta1) * sin(2*\pi/L2 * eta2) \]

Domain: [0,L1] X [0,L2] But we generalize it by taking a transformation Domain: [a,b] X [c,d] --—> Domain: [a',b'] X [c',d'] so the transformation becomes

\[ x1 = (b'-a')/(b-a)*(eta1+alpha1*sin(2*pi*(eta1-a)/(b-a))*sin(2*pi*(eta2-c)/( d-c))) + ( a' b - b' a)/(b- a) \]

\[ x2 = (d' - c')/(d- c) * ( eta2 + alpha2 * sin(2*pi*( eta1-a)/( b-a)) * sin(2*pi*( eta2-c)/( d-c)))+( c' d - d' c)/(d- c) \]

The parameters are:

alpha1 = params(1)
alpha2 = params(2)
a = params(3)
b = params(4)
a' = params(5)
b' = params(6)
c = params(7)
d = params(8)
c' = params(9)
d' = params(10)

Functions/Subroutines
function, public	sll_f_identity_x1 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_identity_x2 (eta1, eta2, params)
	direct mapping More...

function	identity_eta1 (x1, x2, params)
	inverse mapping More...

function	identity_eta2 (x1, x2, params)
	inverse mapping More...

function, public	sll_f_identity_jac11 (eta1, eta2, params)
	jacobian maxtrix More...

function, public	sll_f_identity_jac12 (eta1, eta2, params)
	jacobian maxtrix More...

function, public	sll_f_identity_jac21 (eta1, eta2, params)
	jacobian maxtrix More...

function, public	sll_f_identity_jac22 (eta1, eta2, params)
	jacobian maxtrix More...

function	identity_jac (eta1, eta2, params)
	jacobian ie determinant of jacobian matrix More...

function, public	sll_f_affine_x1 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_affine_x2 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_affine_jac11 (eta1, eta2, params)
	jacobian maxtrix More...

function, public	sll_f_affine_jac12 (eta1, eta2, params)
	jacobian maxtrix More...

function, public	sll_f_affine_jac21 (eta1, eta2, params)
	jacobian maxtrix More...

function, public	sll_f_affine_jac22 (eta1, eta2, params)
	jacobian maxtrix More...

function	affine_jac (eta1, eta2, params)
	jacobian ie determinant of jacobian matrix More...

function, public	sll_f_homography_x1 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_homography_x2 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_homography_jac11 (eta1, eta2, params)
	jacobian maxtrix More...

function, public	sll_f_homography_jac12 (eta1, eta2, params)
	jacobian maxtrix More...

function, public	sll_f_homography_jac21 (eta1, eta2, params)
	jacobian maxtrix More...

function, public	sll_f_homography_jac22 (eta1, eta2, params)
	jacobian maxtrix More...

function	homography_jac (eta1, eta2, params)
	jacobian ie determinant of jacobian matrix More...

function, public	sll_f_rubber_sheeting_x1 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_rubber_sheeting_x2 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_rubber_sheeting_jac11 (eta1, eta2, params)
	jacobian maxtrix More...

function, public	sll_f_rubber_sheeting_jac12 (eta1, eta2, params)
	jacobian maxtrix More...

function, public	sll_f_rubber_sheeting_jac21 (eta1, eta2, params)
	jacobian maxtrix More...

function, public	sll_f_rubber_sheeting_jac22 (eta1, eta2, params)
	jacobian maxtrix More...

function	rubber_sheeting_jac (eta1, eta2, params)
	jacobian ie determinant of jacobian matrix More...

function, public	sll_f_polar_x1 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_polar_x2 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_polar_eta1 (x1, x2, params)
	inverse mapping More...

function, public	sll_f_polar_eta2 (x1, x2, params)
	inverse mapping More...

function, public	sll_f_polar_jac11 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_polar_jac12 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_polar_jac21 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_polar_jac22 (eta1, eta2, params)
	jacobian matrix More...

function	polar_jac (eta1, eta2, params)
	jacobian ie determinant of jacobian matrix More...

function, public	sll_f_polar_shear_x1 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_polar_shear_x2 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_polar_shear_jac11 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_polar_shear_jac12 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_polar_shear_jac21 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_polar_shear_jac22 (eta1, eta2, params)
	jacobian matrix More...

function	polar_shear_jac (eta1, eta2, params)
	jacobian ie determinant of jacobian matrix not computed More...

function, public	sll_f_polygonal_x1 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_polygonal_x2 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_polygonal_jac11 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_polygonal_jac12 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_polygonal_jac21 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_polygonal_jac22 (eta1, eta2, params)
	jacobian matrix More...

function	polygonal_jac (eta1, eta2, params)
	jacobian ie determinant of jacobian matrix not used for the moment (recomputed) More...

function, public	sll_f_sinprod_gen_x1 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_sinprod_gen_x2 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_sinprod_gen_jac11 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_sinprod_gen_jac12 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_sinprod_gen_jac21 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_sinprod_gen_jac22 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_sinprod_gen_jac (eta1, eta2, params)
	jacobian ie determinant of jacobian matrix More...

function, public	sll_f_sinprod_x1 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_sinprod_x2 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_sinprod_jac11 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_sinprod_jac12 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_sinprod_jac21 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_sinprod_jac22 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_sinprod_jac (eta1, eta2, params)
	jacobian ie determinant of jacobian matrix More...

real(8) function	sinprod_x1_rect (eta1, eta2, params)

real(8) function	sinprod_x2_rect (eta1, eta2, params)

real(8) function	sinprod_jac11_rect (eta1, eta2, params)

real(8) function	sinprod_jac12_rect (eta1, eta2, params)

real(8) function	sinprod_jac21_rect (eta1, eta2, params)

real(8) function	sinprod_jac22_rect (eta1, eta2, params)

real(8) function	sinprod_jac_rect (eta1, eta2, params)

real(8) function	sinprod_x1_square (eta1, eta2, params)

real(8) function	sinprod_x2_square (eta1, eta2, params)

real(8) function	sinprod_jac11_square (eta1, eta2, params)

real(8) function	sinprod_jac12_square (eta1, eta2, params)

real(8) function	sinprod_jac21_square (eta1, eta2, params)

real(8) function	sinprod_jac22_square (eta1, eta2, params)

real(8) function	sinprod_jac_square (eta1, eta2, params)

function	test_x1 (eta1, eta2, params)

function	test_x2 (eta1, eta2, params)

function	test_eta1 (x1, x2, params)

function	test_eta2 (x1, x2, params)

function	test_jac11 (eta1, eta2, params)

function	test_jac12 (eta1, eta2, params)

function	test_jac21 (eta1, eta2, params)

function	test_jac22 (eta1, eta2, params)

function	test_jac (eta1, eta2, params)

function, public	sll_f_x1_polar_f (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_x2_polar_f (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_deriv_x1_polar_f_eta1 (eta1, eta2, params)

function, public	sll_f_deriv_x1_polar_f_eta2 (eta1, eta2, params)

function, public	sll_f_deriv_x2_polar_f_eta1 (eta1, eta2, params)

function, public	sll_f_deriv_x2_polar_f_eta2 (eta1, eta2, params)

function, public	sll_f_jacobian_polar_f (eta1, eta2, params)

function, public	sll_f_deriv1_jacobian_polar_f (eta1, eta2, params)

function	linear_map_f (eta, params)

function	linear_map_jac_f (eta, params)

function, public	sll_f_sharped_geo_x1 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_sharped_geo_x2 (eta1, eta2, params)
	direct mapping More...

function, public	sll_f_sharped_geo_jac11 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_sharped_geo_jac12 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_sharped_geo_jac21 (eta1, eta2, params)
	jacobian matrix More...

function, public	sll_f_sharped_geo_jac22 (eta1, eta2, params)
	jacobian matrix More...

function	d_sharped_geo_jac (eta1, eta2, params)
	jacobian ie determinant of jacobian matrix More...

Function/Subroutine Documentation

◆ affine_jac()

function sll_m_common_coordinate_transformations::affine_jac	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

jacobian ie determinant of jacobian matrix

Definition at line 424 of file sll_m_common_coordinate_transformations.F90.

◆ d_sharped_geo_jac()

function sll_m_common_coordinate_transformations::d_sharped_geo_jac	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

jacobian ie determinant of jacobian matrix

Definition at line 2424 of file sll_m_common_coordinate_transformations.F90.

◆ homography_jac()

function sll_m_common_coordinate_transformations::homography_jac	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

jacobian ie determinant of jacobian matrix

Definition at line 565 of file sll_m_common_coordinate_transformations.F90.

◆ identity_eta1()

function sll_m_common_coordinate_transformations::identity_eta1	(	intent(in)	x1,
		intent(in)	x2,
		intent(in)	params
	)

private

inverse mapping

Definition at line 223 of file sll_m_common_coordinate_transformations.F90.

◆ identity_eta2()

function sll_m_common_coordinate_transformations::identity_eta2	(	intent(in)	x1,
		intent(in)	x2,
		intent(in)	params
	)

private

inverse mapping

Definition at line 237 of file sll_m_common_coordinate_transformations.F90.

◆ identity_jac()

function sll_m_common_coordinate_transformations::identity_jac	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

jacobian ie determinant of jacobian matrix

Definition at line 307 of file sll_m_common_coordinate_transformations.F90.

◆ linear_map_f()

function sll_m_common_coordinate_transformations::linear_map_f	(	intent(in)	eta,
		intent(in)	params
	)

private

Definition at line 2134 of file sll_m_common_coordinate_transformations.F90.

◆ linear_map_jac_f()

function sll_m_common_coordinate_transformations::linear_map_jac_f	(	intent(in)	eta,
		intent(in)	params
	)

private

Definition at line 2148 of file sll_m_common_coordinate_transformations.F90.

◆ polar_jac()

function sll_m_common_coordinate_transformations::polar_jac	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

jacobian ie determinant of jacobian matrix

Definition at line 833 of file sll_m_common_coordinate_transformations.F90.

◆ polar_shear_jac()

function sll_m_common_coordinate_transformations::polar_shear_jac	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

jacobian ie determinant of jacobian matrix not computed

Definition at line 948 of file sll_m_common_coordinate_transformations.F90.

◆ polygonal_jac()

function sll_m_common_coordinate_transformations::polygonal_jac	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

jacobian ie determinant of jacobian matrix not used for the moment (recomputed)

Definition at line 1122 of file sll_m_common_coordinate_transformations.F90.

◆ rubber_sheeting_jac()

function sll_m_common_coordinate_transformations::rubber_sheeting_jac	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

jacobian ie determinant of jacobian matrix

Definition at line 697 of file sll_m_common_coordinate_transformations.F90.

◆ sinprod_jac11_rect()

real(8) function sll_m_common_coordinate_transformations::sinprod_jac11_rect	(	real(8), intent(in)	eta1,
		real(8), intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1740 of file sll_m_common_coordinate_transformations.F90.

◆ sinprod_jac11_square()

real(8) function sll_m_common_coordinate_transformations::sinprod_jac11_square	(	real(8), intent(in)	eta1,
		real(8), intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1839 of file sll_m_common_coordinate_transformations.F90.

◆ sinprod_jac12_rect()

real(8) function sll_m_common_coordinate_transformations::sinprod_jac12_rect	(	real(8), intent(in)	eta1,
		real(8), intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1754 of file sll_m_common_coordinate_transformations.F90.

◆ sinprod_jac12_square()

real(8) function sll_m_common_coordinate_transformations::sinprod_jac12_square	(	real(8), intent(in)	eta1,
		real(8), intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1848 of file sll_m_common_coordinate_transformations.F90.

◆ sinprod_jac21_rect()

real(8) function sll_m_common_coordinate_transformations::sinprod_jac21_rect	(	real(8), intent(in)	eta1,
		real(8), intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1768 of file sll_m_common_coordinate_transformations.F90.

◆ sinprod_jac21_square()

real(8) function sll_m_common_coordinate_transformations::sinprod_jac21_square	(	real(8), intent(in)	eta1,
		real(8), intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1856 of file sll_m_common_coordinate_transformations.F90.

◆ sinprod_jac22_rect()

real(8) function sll_m_common_coordinate_transformations::sinprod_jac22_rect	(	real(8), intent(in)	eta1,
		real(8), intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1782 of file sll_m_common_coordinate_transformations.F90.

◆ sinprod_jac22_square()

real(8) function sll_m_common_coordinate_transformations::sinprod_jac22_square	(	real(8), intent(in)	eta1,
		real(8), intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1864 of file sll_m_common_coordinate_transformations.F90.

◆ sinprod_jac_rect()

real(8) function sll_m_common_coordinate_transformations::sinprod_jac_rect	(	real(8), intent(in)	eta1,
		real(8), intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1798 of file sll_m_common_coordinate_transformations.F90.

◆ sinprod_jac_square()

real(8) function sll_m_common_coordinate_transformations::sinprod_jac_square	(	real(8), intent(in)	eta1,
		real(8), intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1874 of file sll_m_common_coordinate_transformations.F90.

◆ sinprod_x1_rect()

real(8) function sll_m_common_coordinate_transformations::sinprod_x1_rect	(	real(8), intent(in)	eta1,
		real(8), intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1705 of file sll_m_common_coordinate_transformations.F90.

◆ sinprod_x1_square()

real(8) function sll_m_common_coordinate_transformations::sinprod_x1_square	(	real(8), intent(in)	eta1,
		real(8), intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1822 of file sll_m_common_coordinate_transformations.F90.

◆ sinprod_x2_rect()

real(8) function sll_m_common_coordinate_transformations::sinprod_x2_rect	(	real(8), intent(in)	eta1,
		real(8), intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1722 of file sll_m_common_coordinate_transformations.F90.

◆ sinprod_x2_square()

real(8) function sll_m_common_coordinate_transformations::sinprod_x2_square	(	real(8), intent(in)	eta1,
		real(8), intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1830 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_affine_jac11()

function, public sll_m_common_coordinate_transformations::sll_f_affine_jac11	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 356 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_affine_jac12()

function, public sll_m_common_coordinate_transformations::sll_f_affine_jac12	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 374 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_affine_jac21()

function, public sll_m_common_coordinate_transformations::sll_f_affine_jac21	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 389 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_affine_jac22()

function, public sll_m_common_coordinate_transformations::sll_f_affine_jac22	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 405 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_affine_x1()

function, public sll_m_common_coordinate_transformations::sll_f_affine_x1	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 321 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_affine_x2()

function, public sll_m_common_coordinate_transformations::sll_f_affine_x2	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 338 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_deriv1_jacobian_polar_f()

function, public sll_m_common_coordinate_transformations::sll_f_deriv1_jacobian_polar_f	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

Definition at line 2097 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_deriv_x1_polar_f_eta1()

function, public sll_m_common_coordinate_transformations::sll_f_deriv_x1_polar_f_eta1	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

Definition at line 2017 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_deriv_x1_polar_f_eta2()

function, public sll_m_common_coordinate_transformations::sll_f_deriv_x1_polar_f_eta2	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

Definition at line 2032 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_deriv_x2_polar_f_eta1()

function, public sll_m_common_coordinate_transformations::sll_f_deriv_x2_polar_f_eta1	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

Definition at line 2048 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_deriv_x2_polar_f_eta2()

function, public sll_m_common_coordinate_transformations::sll_f_deriv_x2_polar_f_eta2	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

Definition at line 2063 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_homography_jac11()

function, public sll_m_common_coordinate_transformations::sll_f_homography_jac11	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 485 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_homography_jac12()

function, public sll_m_common_coordinate_transformations::sll_f_homography_jac12	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 505 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_homography_jac21()

function, public sll_m_common_coordinate_transformations::sll_f_homography_jac21	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 525 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_homography_jac22()

function, public sll_m_common_coordinate_transformations::sll_f_homography_jac22	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 545 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_homography_x1()

function, public sll_m_common_coordinate_transformations::sll_f_homography_x1	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 445 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_homography_x2()

function, public sll_m_common_coordinate_transformations::sll_f_homography_x2	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 465 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_identity_jac11()

function, public sll_m_common_coordinate_transformations::sll_f_identity_jac11	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 251 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_identity_jac12()

function, public sll_m_common_coordinate_transformations::sll_f_identity_jac12	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 265 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_identity_jac21()

function, public sll_m_common_coordinate_transformations::sll_f_identity_jac21	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 279 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_identity_jac22()

function, public sll_m_common_coordinate_transformations::sll_f_identity_jac22	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 293 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_identity_x1()

function, public sll_m_common_coordinate_transformations::sll_f_identity_x1	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 195 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_identity_x2()

function, public sll_m_common_coordinate_transformations::sll_f_identity_x2	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 209 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_jacobian_polar_f()

function, public sll_m_common_coordinate_transformations::sll_f_jacobian_polar_f	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

Definition at line 2079 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_polar_eta1()

function, public sll_m_common_coordinate_transformations::sll_f_polar_eta1	(	intent(in)	x1,
		intent(in)	x2,
		intent(in)	params
	)

inverse mapping

Definition at line 753 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_polar_eta2()

function, public sll_m_common_coordinate_transformations::sll_f_polar_eta2	(	intent(in)	x1,
		intent(in)	x2,
		intent(in)	params
	)

inverse mapping

Definition at line 766 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_polar_jac11()

function, public sll_m_common_coordinate_transformations::sll_f_polar_jac11	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 779 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_polar_jac12()

function, public sll_m_common_coordinate_transformations::sll_f_polar_jac12	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 793 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_polar_jac21()

function, public sll_m_common_coordinate_transformations::sll_f_polar_jac21	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 806 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_polar_jac22()

function, public sll_m_common_coordinate_transformations::sll_f_polar_jac22	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 820 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_polar_shear_jac11()

function, public sll_m_common_coordinate_transformations::sll_f_polar_shear_jac11	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 886 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_polar_shear_jac12()

function, public sll_m_common_coordinate_transformations::sll_f_polar_shear_jac12	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 902 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_polar_shear_jac21()

function, public sll_m_common_coordinate_transformations::sll_f_polar_shear_jac21	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 917 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_polar_shear_jac22()

function, public sll_m_common_coordinate_transformations::sll_f_polar_shear_jac22	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 933 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_polar_shear_x1()

function, public sll_m_common_coordinate_transformations::sll_f_polar_shear_x1	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 856 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_polar_shear_x2()

function, public sll_m_common_coordinate_transformations::sll_f_polar_shear_x2	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 871 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_polar_x1()

function, public sll_m_common_coordinate_transformations::sll_f_polar_x1	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 727 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_polar_x2()

function, public sll_m_common_coordinate_transformations::sll_f_polar_x2	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 740 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_polygonal_jac11()

function, public sll_m_common_coordinate_transformations::sll_f_polygonal_jac11	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 1018 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_polygonal_jac12()

function, public sll_m_common_coordinate_transformations::sll_f_polygonal_jac12	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 1042 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_polygonal_jac21()

function, public sll_m_common_coordinate_transformations::sll_f_polygonal_jac21	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 1069 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_polygonal_jac22()

function, public sll_m_common_coordinate_transformations::sll_f_polygonal_jac22	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 1093 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_polygonal_x1()

function, public sll_m_common_coordinate_transformations::sll_f_polygonal_x1	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 972 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_polygonal_x2()

function, public sll_m_common_coordinate_transformations::sll_f_polygonal_x2	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 995 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_rubber_sheeting_jac11()

function, public sll_m_common_coordinate_transformations::sll_f_rubber_sheeting_jac11	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 629 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_rubber_sheeting_jac12()

function, public sll_m_common_coordinate_transformations::sll_f_rubber_sheeting_jac12	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 646 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_rubber_sheeting_jac21()

function, public sll_m_common_coordinate_transformations::sll_f_rubber_sheeting_jac21	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 663 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_rubber_sheeting_jac22()

function, public sll_m_common_coordinate_transformations::sll_f_rubber_sheeting_jac22	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian maxtrix

Definition at line 680 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_rubber_sheeting_x1()

function, public sll_m_common_coordinate_transformations::sll_f_rubber_sheeting_x1	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 591 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_rubber_sheeting_x2()

function, public sll_m_common_coordinate_transformations::sll_f_rubber_sheeting_x2	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 610 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_sharped_geo_jac11()

function, public sll_m_common_coordinate_transformations::sll_f_sharped_geo_jac11	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 2277 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_sharped_geo_jac12()

function, public sll_m_common_coordinate_transformations::sll_f_sharped_geo_jac12	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 2314 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_sharped_geo_jac21()

function, public sll_m_common_coordinate_transformations::sll_f_sharped_geo_jac21	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 2352 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_sharped_geo_jac22()

function, public sll_m_common_coordinate_transformations::sll_f_sharped_geo_jac22	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 2388 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_sharped_geo_x1()

function, public sll_m_common_coordinate_transformations::sll_f_sharped_geo_x1	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 2204 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_sharped_geo_x2()

function, public sll_m_common_coordinate_transformations::sll_f_sharped_geo_x2	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 2241 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_sinprod_gen_jac()

function, public sll_m_common_coordinate_transformations::sll_f_sinprod_gen_jac	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian ie determinant of jacobian matrix

Definition at line 1484 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_sinprod_gen_jac11()

function, public sll_m_common_coordinate_transformations::sll_f_sinprod_gen_jac11	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 1304 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_sinprod_gen_jac12()

function, public sll_m_common_coordinate_transformations::sll_f_sinprod_gen_jac12	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 1349 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_sinprod_gen_jac21()

function, public sll_m_common_coordinate_transformations::sll_f_sinprod_gen_jac21	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 1394 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_sinprod_gen_jac22()

function, public sll_m_common_coordinate_transformations::sll_f_sinprod_gen_jac22	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 1438 of file sll_m_common_coordinate_transformations.F90.

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◆ sll_f_sinprod_gen_x1()

function, public sll_m_common_coordinate_transformations::sll_f_sinprod_gen_x1	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 1181 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_sinprod_gen_x2()

function, public sll_m_common_coordinate_transformations::sll_f_sinprod_gen_x2	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 1225 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_sinprod_jac()

function, public sll_m_common_coordinate_transformations::sll_f_sinprod_jac	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian ie determinant of jacobian matrix

Definition at line 1675 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_sinprod_jac11()

function, public sll_m_common_coordinate_transformations::sll_f_sinprod_jac11	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 1599 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_sinprod_jac12()

function, public sll_m_common_coordinate_transformations::sll_f_sinprod_jac12	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 1618 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_sinprod_jac21()

function, public sll_m_common_coordinate_transformations::sll_f_sinprod_jac21	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 1637 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_sinprod_jac22()

function, public sll_m_common_coordinate_transformations::sll_f_sinprod_jac22	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

jacobian matrix

Definition at line 1656 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_sinprod_x1()

function, public sll_m_common_coordinate_transformations::sll_f_sinprod_x1	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 1526 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_sinprod_x2()

function, public sll_m_common_coordinate_transformations::sll_f_sinprod_x2	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 1545 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_x1_polar_f()

function, public sll_m_common_coordinate_transformations::sll_f_x1_polar_f	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 1989 of file sll_m_common_coordinate_transformations.F90.

◆ sll_f_x2_polar_f()

function, public sll_m_common_coordinate_transformations::sll_f_x2_polar_f	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

direct mapping

Definition at line 2003 of file sll_m_common_coordinate_transformations.F90.

◆ test_eta1()

function sll_m_common_coordinate_transformations::test_eta1	(	intent(in)	x1,
		intent(in)	x2,
		intent(in)	params
	)

private

Definition at line 1912 of file sll_m_common_coordinate_transformations.F90.

◆ test_eta2()

function sll_m_common_coordinate_transformations::test_eta2	(	intent(in)	x1,
		intent(in)	x2,
		intent(in)	params
	)

private

Definition at line 1920 of file sll_m_common_coordinate_transformations.F90.

◆ test_jac()

function sll_m_common_coordinate_transformations::test_jac	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1962 of file sll_m_common_coordinate_transformations.F90.

◆ test_jac11()

function sll_m_common_coordinate_transformations::test_jac11	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1929 of file sll_m_common_coordinate_transformations.F90.

◆ test_jac12()

function sll_m_common_coordinate_transformations::test_jac12	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1937 of file sll_m_common_coordinate_transformations.F90.

◆ test_jac21()

function sll_m_common_coordinate_transformations::test_jac21	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1945 of file sll_m_common_coordinate_transformations.F90.

◆ test_jac22()

function sll_m_common_coordinate_transformations::test_jac22	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1953 of file sll_m_common_coordinate_transformations.F90.

◆ test_x1()

function sll_m_common_coordinate_transformations::test_x1	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1894 of file sll_m_common_coordinate_transformations.F90.

◆ test_x2()

function sll_m_common_coordinate_transformations::test_x2	(	intent(in)	eta1,
		intent(in)	eta2,
		intent(in)	params
	)

private

Definition at line 1903 of file sll_m_common_coordinate_transformations.F90.

Description

Functions/Subroutines

Function/Subroutine Documentation

◆ affine_jac()

◆ d_sharped_geo_jac()

◆ homography_jac()

◆ identity_eta1()

◆ identity_eta2()

◆ identity_jac()

◆ linear_map_f()

◆ linear_map_jac_f()

◆ polar_jac()

◆ polar_shear_jac()

◆ polygonal_jac()

◆ rubber_sheeting_jac()

◆ sinprod_jac11_rect()

◆ sinprod_jac11_square()

◆ sinprod_jac12_rect()

◆ sinprod_jac12_square()

◆ sinprod_jac21_rect()

◆ sinprod_jac21_square()

◆ sinprod_jac22_rect()

◆ sinprod_jac22_square()

◆ sinprod_jac_rect()

◆ sinprod_jac_square()

◆ sinprod_x1_rect()

◆ sinprod_x1_square()

◆ sinprod_x2_rect()

◆ sinprod_x2_square()

◆ sll_f_affine_jac11()

◆ sll_f_affine_jac12()

◆ sll_f_affine_jac21()

◆ sll_f_affine_jac22()

◆ sll_f_affine_x1()

◆ sll_f_affine_x2()

◆ sll_f_deriv1_jacobian_polar_f()

◆ sll_f_deriv_x1_polar_f_eta1()

◆ sll_f_deriv_x1_polar_f_eta2()

◆ sll_f_deriv_x2_polar_f_eta1()

◆ sll_f_deriv_x2_polar_f_eta2()

◆ sll_f_homography_jac11()

◆ sll_f_homography_jac12()

◆ sll_f_homography_jac21()

◆ sll_f_homography_jac22()

◆ sll_f_homography_x1()

◆ sll_f_homography_x2()

◆ sll_f_identity_jac11()

◆ sll_f_identity_jac12()

◆ sll_f_identity_jac21()

◆ sll_f_identity_jac22()

◆ sll_f_identity_x1()

◆ sll_f_identity_x2()

◆ sll_f_jacobian_polar_f()

◆ sll_f_polar_eta1()

◆ sll_f_polar_eta2()

◆ sll_f_polar_jac11()

◆ sll_f_polar_jac12()

◆ sll_f_polar_jac21()

◆ sll_f_polar_jac22()

◆ sll_f_polar_shear_jac11()

◆ sll_f_polar_shear_jac12()

◆ sll_f_polar_shear_jac21()

◆ sll_f_polar_shear_jac22()

◆ sll_f_polar_shear_x1()

◆ sll_f_polar_shear_x2()

◆ sll_f_polar_x1()

◆ sll_f_polar_x2()

◆ sll_f_polygonal_jac11()

◆ sll_f_polygonal_jac12()

◆ sll_f_polygonal_jac21()

◆ sll_f_polygonal_jac22()

◆ sll_f_polygonal_x1()

◆ sll_f_polygonal_x2()

◆ sll_f_rubber_sheeting_jac11()

◆ sll_f_rubber_sheeting_jac12()

◆ sll_f_rubber_sheeting_jac21()

◆ sll_f_rubber_sheeting_jac22()

◆ sll_f_rubber_sheeting_x1()

◆ sll_f_rubber_sheeting_x2()

◆ sll_f_sharped_geo_jac11()