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math.c
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/* Panorama_Tools - Generate, Edit and Convert Panoramic Images
Copyright (C) 1998,1999 - Helmut Dersch [email protected]
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this software; see the file COPYING. If not, a copy
can be downloaded from http://www.gnu.org/licenses/gpl.html, or
obtained by writing to the Free Software Foundation, Inc.,
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. */
/*------------------------------------------------------------*/
#include "filter.h"
#include <float.h>
#include "f2c.h"
#include "PaniniGeneral.h"
#define R_EPS 1.0e-6
#define MAXITER 100
#include <assert.h>
#ifndef abs
#define abs(a) ( (a) >= 0 ? (a) : -(a) )
#endif
#if defined _MSC_VER && _MSC_VER<1900
#define isnan(a) _isnan(a)
#define isinf(a) (_fpclass(a) == _FPCLASS_NINF || _fpclass(a) == _FPCLASS_PINF)
#endif
void matrix_matrix_mult ( double m1[3][3],double m2[3][3],double result[3][3]);
int polzeros_();
void cubeZero( double *a, int *n, double *root );
void squareZero( double *a, int *n, double *root );
double cubeRoot( double x );
//------------------------- Some auxilliary math functions --------------------------------------------
// atanh is not available on MSVC until Visual Studio 2012. Use the atanh routine from gsl.
#if defined _MSC_VER && _MSC_VER < 1700
#define GSL_DBL_EPSILON 2.2204460492503131e-16
#define GSL_SQRT_DBL_EPSILON 1.4901161193847656e-08
static double
log1p (const double x)
{
volatile double y;
y = 1 + x;
return log(y) - ((y-1)-x)/y ; /* cancels errors with IEEE arithmetic */
}
static double
atanh (const double x)
{
double a = fabs (x);
double s = (x < 0) ? -1 : 1;
if (a > 1)
{
//return NAN;
return 0;
}
else if (a == 1)
{
//return (x < 0) ? GSL_NEGINF : GSL_POSINF;
return (x < 0) ? -1e300 : 1e300;
}
else if (a >= 0.5)
{
return s * 0.5 * log1p (2 * a / (1 - a));
}
else if (a > GSL_DBL_EPSILON)
{
return s * 0.5 * log1p (2 * a + 2 * a * a / (1 - a));
}
else
{
return x;
}
}
#endif
void matrix_mult( double m[3][3], double vector[3] )
{
register int i;
register double v0 = vector[0];
register double v1 = vector[1];
register double v2 = vector[2];
for(i=0; i<3; i++)
{
vector[i] = m[i][0] * v0 + m[i][1] * v1 + m[i][2] * v2;
}
}
void matrix_inv_mult( double m[3][3], double vector[3] )
{
register int i;
register double v0 = vector[0];
register double v1 = vector[1];
register double v2 = vector[2];
for(i=0; i<3; i++)
{
vector[i] = m[0][i] * v0 + m[1][i] * v1 + m[2][i] * v2;
}
}
void matrix_matrix_mult( double m1[3][3],double m2[3][3],double result[3][3])
{
register int i,k;
for(i=0;i<3;i++)
{
for(k=0; k<3; k++)
{
result[i][k] = m1[i][0] * m2[0][k] + m1[i][1] * m2[1][k] + m1[i][2] * m2[2][k];
}
}
}
// Set matrix elements based on Euler angles a, b, c
void SetMatrix( double a, double b, double c , double m[3][3], int cl )
{
double mx[3][3], my[3][3], mz[3][3], dummy[3][3];
// Calculate Matrices;
mx[0][0] = 1.0 ; mx[0][1] = 0.0 ; mx[0][2] = 0.0;
mx[1][0] = 0.0 ; mx[1][1] = cos(a) ; mx[1][2] = sin(a);
mx[2][0] = 0.0 ; mx[2][1] =-mx[1][2] ; mx[2][2] = mx[1][1];
my[0][0] = cos(b); my[0][1] = 0.0 ; my[0][2] =-sin(b);
my[1][0] = 0.0 ; my[1][1] = 1.0 ; my[1][2] = 0.0;
my[2][0] = -my[0][2]; my[2][1] = 0.0 ; my[2][2] = my[0][0];
mz[0][0] = cos(c) ; mz[0][1] = sin(c) ; mz[0][2] = 0.0;
mz[1][0] =-mz[0][1] ; mz[1][1] = mz[0][0] ; mz[1][2] = 0.0;
mz[2][0] = 0.0 ; mz[2][1] = 0.0 ; mz[2][2] = 1.0;
if( cl )
matrix_matrix_mult( mz, mx, dummy);
else
matrix_matrix_mult( mx, mz, dummy);
matrix_matrix_mult( dummy, my, m);
}
// Do 3D-coordinate Transformation
void doCoordinateTransform( CoordInfo *ci, tMatrix *t )
{
double m[3][3],a,b,c;
int i;
double mx[3][3], my[3][3], mz[3][3], dummy[3][3];
// Calculate Matrices;
a = DEG_TO_RAD( t->alpha );
b = DEG_TO_RAD( t->beta );
c = DEG_TO_RAD( t->gamma );
mx[0][0] = 1.0 ; mx[0][1] = 0.0 ; mx[0][2] = 0.0;
mx[1][0] = 0.0 ; mx[1][1] = cos(a) ; mx[1][2] = sin(a);
mx[2][0] = 0.0 ; mx[2][1] =-mx[1][2] ; mx[2][2] = mx[1][1];
my[0][0] = cos(b); my[0][1] = 0.0 ; my[0][2] =-sin(b);
my[1][0] = 0.0 ; my[1][1] = 1.0 ; my[1][2] = 0.0;
my[2][0] = -my[0][2]; my[2][1] = 0.0 ; my[2][2] = my[0][0];
mz[0][0] = cos(c) ; mz[0][1] = sin(c) ; mz[0][2] = 0.0;
mz[1][0] =-mz[0][1] ; mz[1][1] = mz[0][0] ; mz[1][2] = 0.0;
mz[2][0] = 0.0 ; mz[2][1] = 0.0 ; mz[2][2] = 1.0;
matrix_matrix_mult( my, mz, dummy);
matrix_matrix_mult( mx, dummy, m);
// Scale
for(i=0; i<3; i++)
ci->x[i] *= t->scale;
// Do shift
for(i=0; i<3; i++)
ci->x[i] += t->x_shift[i];
// Do rotation
#if 0
SetMatrix( DEG_TO_RAD( t->alpha ) ,
DEG_TO_RAD( t->beta ) ,
DEG_TO_RAD( t->gamma ) ,
m, 0 );
#endif
matrix_inv_mult( m, ci->x );
}
void SettMatrixDefaults( tMatrix *t )
{
int i;
t->alpha = t->beta = t->gamma = 0.0;
for(i=0; i<3; i++)
t->x_shift[i] = 0.0;
t->scale = 1.0;
}
//------------------------------- Transformation functions --------------------------------------------
#define distanceparam (*((double*)params))
#define shift (*((double*)params))
#define var0 ((double*)params)[0]
#define var1 ((double*)params)[1]
#define var2 ((double*)params)[2]
#define var3 ((double*)params)[3]
#define mp ((struct MakeParams*)params)
// execute a stack of functions stored in stack
void execute_stack ( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
register double xd = x_dest,
yd = y_dest;
register struct fDesc* stack = (struct fDesc *) params;;
while( (stack->func) != NULL )
{
(stack->func) ( xd, yd, x_src, y_src, stack->param );
xd = *x_src;
yd = *y_src;
stack++;
}
}
int execute_stack_new( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
register double xd = x_dest,
yd = y_dest;
register struct fDesc* stack = (struct fDesc *) params;
while( (stack->func) != NULL )
{
if ( (stack->func) ( xd, yd, x_src, y_src, stack->param ) ) {
// printf("Execute stack %f %f %f %f\n", xd, yd, *x_src, *y_src);
xd = *x_src;
yd = *y_src;
stack++;
} else {
return 0;
}
}
return 1;
}
// Rotate equirectangular image
int rotate_erect( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// params: double 180degree_turn(screenpoints), double turn(screenpoints);
*x_src = x_dest + var1;
while( *x_src < - var0 )
*x_src += 2 * var0;
while( *x_src > var0 )
*x_src -= 2 * var0;
*y_src = y_dest ;
return 1;
}
// Calculate inverse 4th order polynomial correction using Newton
// Don't use on large image (slow)!
int inv_radial( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// params: double coefficients[4]
register double rs, rd, f, scale;
int iter = 0;
rd = (sqrt( x_dest*x_dest + y_dest*y_dest )) / ((double*)params)[4]; // Normalized
rs = rd;
f = (((((double*)params)[3] * rs + ((double*)params)[2]) * rs +
((double*)params)[1]) * rs + ((double*)params)[0]) * rs;
while( abs(f - rd) > R_EPS && iter++ < MAXITER )
{
rs = rs - (f - rd) / ((( 4 * ((double*)params)[3] * rs + 3 * ((double*)params)[2]) * rs +
2 * ((double*)params)[1]) * rs + ((double*)params)[0]);
f = (((((double*)params)[3] * rs + ((double*)params)[2]) * rs +
((double*)params)[1]) * rs + ((double*)params)[0]) * rs;
}
scale = (rd!=0.0) ? rs / rd : 1.0f;
// printf("scale = %lg iter = %d\n", scale,iter);
*x_src = x_dest * scale ;
*y_src = y_dest * scale ;
return 1;
}
int inv_vertical( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// params: double coefficients[4]
register double rs, rd, f, scale;
int iter = 0;
rd = abs( y_dest ) / ((double*)params)[4]; // Normalized
rs = rd;
f = (((((double*)params)[3] * rs + ((double*)params)[2]) * rs +
((double*)params)[1]) * rs + ((double*)params)[0]) * rs;
while( abs(f - rd) > R_EPS && iter++ < MAXITER )
{
rs = rs - (f - rd) / ((( 4 * ((double*)params)[3] * rs + 3 * ((double*)params)[2]) * rs +
2 * ((double*)params)[1]) * rs + ((double*)params)[0]);
f = (((((double*)params)[3] * rs + ((double*)params)[2]) * rs +
((double*)params)[1]) * rs + ((double*)params)[0]) * rs;
}
scale = rs / rd;
// printf("scale = %lg iter = %d\n", scale,iter);
*x_src = x_dest ;
*y_src = y_dest * scale ;
return 1;
}
int resize( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// params: double scale_horizontal, double scale_vertical;
*x_src = x_dest * var0;
*y_src = y_dest * var1;
return 1;
}
int tiltInverse( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
//
// This is really the inverse transformation
// printf( "Entered invtilt function \n");
double theta = mp->tilt[0]; // use the tilt angle specified by the 'L' parameter
double sigma = mp->tilt[1]; // use the tilt angle specified by the 'L' parameter
double phi = mp->tilt[2];
double scale = mp->tilt[3];
double v[3]; // 3D projective coordinate vector
double m_tilt[3][3]; // tilt matrix
double m_rotate[3][3]; // tilt matrix
double xmax = mp->im->width/2; // maximum y value is image width divided by 2
double z0;
double FOV = DEG_TO_RAD(mp->im->hfov/scale);
double m_slant[3][3]; // slant matrix
// printf("Tilt Inverse %5.2f %5.2f %5.2f, %5.2f\n", x_dest, y_dest, theta, sigma);
// These operations are based on the typical projection of a point to a camera.
// But, we want the projection to happen without translation, so we need to subtract
// the coordinates of 0,0 projected... that is why the [1][2], [2][2] components
// of the matrix are 0 or 1 in the tilt-x and tilt-y
// Tilt (around X) INVERSE. The matrix does not require the [1][2], [2][2]
// because it is tilted in its center
m_tilt[0][0] = 1; m_tilt[0][1] = 0; m_tilt[0][2] = 0;
m_tilt[1][0] = 0; m_tilt[1][1] = cos(theta); m_tilt[1][2] = 0; // sin(theta);
m_tilt[2][0] = 0; m_tilt[2][1] = -sin(theta); m_tilt[2][2] = 1; //cos(theta);
// Tilt (around Y) INVERSE.
// [0][2] and [2][2] are changed to tilt on center of image. See above
m_slant[0][0] = cos(sigma); m_slant[0][1] = 0; m_slant[0][2] = 0; //-sin(sigma);
m_slant[1][0] = 0; m_slant[1][1] = 1; m_slant[1][2] = 0;
m_slant[2][0] = sin(sigma); m_slant[2][1] = 0; m_slant[2][2] = 1; //cos(sigma);
// Slant (around z)
// Tilt (around z) INVERSE
m_rotate[0][0] = cos(phi); m_rotate[0][1] = sin(phi); m_rotate[0][2] = 0;
m_rotate[1][0] = -sin(phi); m_rotate[1][1] = cos(phi); m_rotate[1][2] = 0;
m_rotate[2][0] = 0; m_rotate[2][1] = 0; m_rotate[2][2]= 1;
z0 = xmax/tan(FOV/2); // FOV is full angle FOV in radians
// printf("Values Forward %5.2f %5.2f %5.2f, %5.2f\n", x_dest, y_dest, distanceparam, z0);
// z0 is distance to image from center of projection
//printf("z0 is %f \n", z0);
// Now you have [x_dest, y_dest, z1]'. Multiply that vector by M, the adjusted tilt matrix
v[0] = x_dest;
v[1] = y_dest;
v[2] = z0;
matrix_mult(m_rotate,v);
matrix_mult(m_slant,v);
matrix_mult(m_tilt,v);
// Now project into xy plane
*x_src = v[0]* z0 /v[2];
*y_src = v[1]* z0 /v[2];
// THIS IS THE OPTIMIZED VERSION with no matrices multiplications. ..
#ifdef OPTIMIZED
double x = x_dest;
double y = y_dest;
double above = (x * cos(phi) + y * sin(phi)) * cos (sigma);
double below1 = (x * cos(phi) + y * sin(phi)) * sin(sigma);
double below2 = - sin(theta) * (y * cos(phi) - x * sin(phi));
double x4 = z0* above / (below1 + below2 + z0);
above = (-x * sin (phi) + y * cos(phi)) * cos(theta);
below1 = (x * cos(phi) + y * sin(phi)) * sin (sigma);
below2 = (-x * sin(phi) + y * cos(phi)) * sin(theta);
double y4 = z0 * above / (below1 - below2 + z0);
#endif
// printf("x4 %6.2f x_c %6.2f\n", x4, *x_src);
// printf("x4 %6.2f x_c %6.2f\n", y4, *y_src);
return 1;
}
// Dev: inverse tilt function. Substitute correct matrix for "un-tilting"
int tiltForward( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// INVERSE is a misnomer --panotools ##$&^
// This is really the forward transformation
// printf( "Entered invtilt function \n");
double phi = mp->tilt[0]; // use the tilt angle specified by the 'L' parameter (already in radians)
double phi2 = mp->tilt[1]; // use the tilt angle specified by the 'L' parameter (already in radians)
double phi3 = mp->tilt[2];
double scale = mp->tilt[3];
double v[3]; // 3D projective coordinate vector
double m_tilt[3][3]; // tilt matrix
double xmax = mp->im->width/2; // maximum y value is image width divided by 2
double z0, z1, s;
double FOV = DEG_TO_RAD(mp->im->hfov/scale);
double m_slant[3][3]; // slant matrix
double m_rotate[3][3]; // tilt matrix
// printf("Tilt Forward %5.2f %5.2f angles %5.2f, %5.2f, %5.2f\n", x_dest, y_dest, phi, phi2, phi3);
// TILT TO STRAIGHT matrix (tilt2() in MATLAB). Really and UN-TILTING matrix
// FORWARD
m_tilt[0][0] = 1; m_tilt[0][1] = 0; m_tilt[0][2] = 0;
m_tilt[1][0] = 0; m_tilt[1][1] = 1/cos(phi); m_tilt[1][2] = 0;
m_tilt[2][0] = 0; m_tilt[2][1] = tan(phi); m_tilt[2][2] = 1;
m_slant[0][0] = 1/cos(phi2); m_slant[0][1] = 0; m_slant[0][2] = 0;
m_slant[1][0] = 0; m_slant[1][1] = 1; m_slant[1][2] = 0;
m_slant[2][0] = -sin(phi2)/cos(phi2); m_slant[2][1] = 0; m_slant[2][2] = 1;
// FORWARD
m_rotate[0][0] = cos(phi3); m_rotate[0][1] = -sin(phi3); m_rotate[0][2] = 0;
m_rotate[1][0] = sin(phi3); m_rotate[1][1] = cos(phi3); m_rotate[1][2] = 0;
m_rotate[2][0] = 0; m_rotate[2][1] = 0; m_rotate[2][2]= 1;
z0 = xmax/tan(FOV/2); // FOV is full angle FOV in radians
// z0 is distance to image from center of projection
// First step, undo the projection of the point
z1 = (z0 * z0) /(x_dest * (-sin(phi2)/cos(phi2)) + y_dest * tan(phi) + z0);
// s = z1 / z0;
s = z0 /(x_dest * (-sin(phi2)/cos(phi2)) + y_dest * sin(phi)/cos(phi) + z0);
z1 = (z0* z0) /(x_dest * (-sin(phi2)/cos(phi2)) + y_dest * sin(phi)/cos(phi) + z0);
//(y_dest * tan(phi) + x_dest * tan(phi2) + z0);
//s = z0 / (y_dest * tan(phi) + z0); // s is a scaling factor ...
//printf("z0 is %f \n", z0);
// Now you have [x_dest, y_dest, z1]'. Multiply that vector by M, the adjusted tilt matrix
v[0] = s* x_dest;
v[1] = s* y_dest;
v[2] = z1;
// matrix_mult(m_tilt,v);
matrix_mult(m_tilt,v);
matrix_mult(m_slant,v);
matrix_mult(m_rotate,v);
*x_src = v[0] ; // convert back to cartesian coordinates
*y_src = v[1];
// printf( "Entered tiltforward function tilt z0,z1,v[21] (%f,%f, %f)\n", z0, z1, v[2]);
// printf( "Entered invtiltb function in (%6.2f %6.2f) out (%6.2f %6.2f)\n", x_dest, y_dest, *x_src, *y_src);
// Uncommenting code below causes tilt function to do nothing:
// *x_src = x_dest;
// *y_src = y_dest;
return 1;
}
int shear( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// params: double shear_horizontal, double shear_vertical;
// printf( "Entered shear function \n");
*x_src = x_dest + var0 * y_dest;
*y_src = y_dest + var1 * x_dest;
return 1;
}
int shearInv( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// params: double shear_horizontal, double shear_vertical;
// printf( "Entered shear inv function \n");
*y_src = (y_dest - var1 * x_dest) / (1 - var1 * var0);
*x_src = (x_dest - var0 * *y_src);
return 1;
}
int horiz( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// params: double horizontal shift
*x_src = x_dest + shift;
*y_src = y_dest;
return 1;
}
int vert( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// params: double vertical shift
*x_src = x_dest;
*y_src = y_dest + shift;
return 1;
}
int radial( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// params: double coefficients[4], scale, correction_radius
register double r, scale;
r = (sqrt( x_dest*x_dest + y_dest*y_dest )) / ((double*)params)[4];
if( r < ((double*)params)[5] )
{
scale = ((((double*)params)[3] * r + ((double*)params)[2]) * r +
((double*)params)[1]) * r + ((double*)params)[0];
}
else
scale = 1000.0;
*x_src = x_dest * scale ;
*y_src = y_dest * scale ;
return 1;
}
int vertical( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// params: double coefficients[4]
register double r, scale;
r = y_dest / ((double*)params)[4];
if( r < 0.0 ) r = -r;
scale = ((((double*)params)[3] * r + ((double*)params)[2]) * r +
((double*)params)[1]) * r + ((double*)params)[0];
*x_src = x_dest;
*y_src = y_dest * scale ;
return 1;
}
int deregister( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// params: double coefficients[4]
register double r, scale;
r = y_dest / ((double*)params)[4];
if( r < 0.0 ) r = -r;
scale = (((double*)params)[3] * r + ((double*)params)[2]) * r +
((double*)params)[1] ;
*x_src = x_dest + abs( y_dest ) * scale;
*y_src = y_dest ;
return 1;
}
int persp_sphere( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params : double Matrix[3][3], double distanceparam
register double theta,s,r;
double v[3];
#if 0 // old
theta = sqrt( x_dest * x_dest + y_dest * y_dest ) / *((double*) ((void**)params)[1]);
phi = atan2( y_dest , x_dest );
v[0] = *((double*) ((void**)params)[1]) * sin( theta ) * cos( phi );
v[1] = *((double*) ((void**)params)[1]) * sin( theta ) * sin( phi );
v[2] = *((double*) ((void**)params)[1]) * cos( theta );
matrix_inv_mult( (double(*)[3]) ((void**)params)[0], v );
theta = atan2( sqrt( v[0]*v[0] + v[1]*v[1] ), v[2] );
phi = atan2( v[1], v[0] );
*x_src = *((double*) ((void**)params)[1]) * theta * cos( phi );
*y_src = *((double*) ((void**)params)[1]) * theta * sin( phi );
#endif
r = sqrt( x_dest * x_dest + y_dest * y_dest );
theta = r / *((double*) ((void**)params)[1]);
if( r == 0.0 )
s = 0.0;
else
s = sin( theta ) / r;
v[0] = s * x_dest ;
v[1] = s * y_dest ;
v[2] = cos( theta );
matrix_inv_mult( (double(*)[3]) ((void**)params)[0], v );
r = sqrt( v[0]*v[0] + v[1]*v[1] );
if( r == 0.0 )
theta = 0.0;
else
theta = *((double*) ((void**)params)[1]) * atan2( r, v[2] ) / r;
*x_src = theta * v[0];
*y_src = theta * v[1];
return 1;
}
int persp_rect( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// params : double Matrix[3][3], double distanceparam, double x-offset, double y-offset
double v[3];
v[0] = x_dest + *((double*) ((void**)params)[2]);
v[1] = y_dest + *((double*) ((void**)params)[3]);
v[2] = *((double*) ((void**)params)[1]);
matrix_inv_mult( (double(*)[3]) ((void**)params)[0], v );
*x_src = v[0] * *((double*) ((void**)params)[1]) / v[2] ;
*y_src = v[1] * *((double*) ((void**)params)[1]) / v[2] ;
return 1;
}
int rect_pano( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
*x_src = distanceparam * tan( x_dest / distanceparam ) ;
*y_src = y_dest / cos( x_dest / distanceparam );
return 1;
}
int pano_rect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
*x_src = distanceparam * atan ( x_dest / distanceparam );
*y_src = y_dest * cos( *x_src / distanceparam );
return 1;
}
int rect_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam
register double phi, theta;
phi = x_dest / distanceparam;
theta = - y_dest / distanceparam + PI / 2.0;
if(theta < 0)
{
theta = - theta;
phi += PI;
}
if(theta > PI)
{
theta = PI - (theta - PI);
phi += PI;
}
#if 0
v[2] = *((double*)params) * sin( theta ) * cos( phi ); // x' -> z
v[0] = *((double*)params) * sin( theta ) * sin( phi ); // y' -> x
v[1] = *((double*)params) * cos( theta ); // z' -> y
phi = atan2( v[1], v[0] );
// old:
// theta = atan2( sqrt( v[0]*v[0] + v[1]*v[1] ) , v[2] );
// rho = *((double*)params) * tan( theta );
// new:
rho = *((double*)params) * sqrt( v[0]*v[0] + v[1]*v[1] ) / v[2];
*x_src = rho * cos( phi );
*y_src = rho * sin( phi );
#endif
#if 1
*x_src = distanceparam * tan(phi);
*y_src = distanceparam / (tan( theta ) * cos(phi));
#endif
// normalize phi to be in the -PI, PI range
while(phi <= -PI)
phi += 2*PI;
while(phi > PI)
phi -= 2*PI;
// check if the point is "in front" of the camera
if (phi < -PI/2.0 || phi > PI/2.0) {
// behind, transform considered invalid
return 0;
} else
return 1;
// normalize phi to be in the -PI, PI range
while(phi <= -PI)
phi += 2*PI;
while(phi > PI)
phi -= 2*PI;
// check if the point is "in front" of the camera
if (phi < -PI/2.0 || phi > PI/2.0) {
// behind, transform considered invalid
return 0;
} else
return 1;
}
// This is the cylindrical projection
int pano_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam
*x_src = x_dest;
*y_src = distanceparam * tan( y_dest / distanceparam);
return 1;
}
int erect_pano( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam
*x_src = x_dest;
*y_src = distanceparam * atan( y_dest / distanceparam);
return 1;
}
/** convert from erect to lambert azimuthal */
int lambertazimuthal_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: distanceparam
double phi, lambda,k1;
lambda = x_dest/distanceparam;
phi = y_dest/distanceparam;
if (abs(cos(phi) * cos(lambda) + 1.0) <= EPSLN) {
*x_src = distanceparam * 2 ;
*y_src = 0;
return 0;
}
k1 = sqrt(2.0 / (1 + cos(phi) * cos(lambda)));
*x_src = distanceparam * k1 * cos(phi) * sin (lambda);
*y_src = distanceparam * k1 * sin(phi);
return 1;
}
/** convert from lambert azimuthal to erect */
int erect_lambertazimuthal( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
double x, y, ro,c;
x = x_dest/distanceparam;
y = y_dest/distanceparam;
assert(! isnan(x));
assert(! isnan(y));
if (fabs(x) > PI || fabs(y) > PI) {
*y_src = 0;
*x_src = 0;
return 0;
}
ro = hypot(x, y);
if (fabs(ro) <= EPSLN)
{
*y_src = 0;
*x_src = 0;
return 1;
}
c = 2 * asin(ro / 2.0);
*y_src = distanceparam * asin( (y * sin(c)) / ro);
if (fabs(ro * cos(c)) <= EPSLN ) {
*x_src = 0;
return 1;
}
*x_src = distanceparam * atan2( x * sin(c), (ro * cos(c)));
return 1;
}
/** convert from erect to hammer */
int hammer_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
if(lambertazimuthal_erect(x_dest/2.0, y_dest, x_src, y_src, params))
{
*x_src *= 2.0;
return 1;
}
else
{
*x_src=0;
*y_src=0;
return 0;
};
}
/** convert from hammer to erect */
int erect_hammer( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
double x, y, z;
x = x_dest/distanceparam;
y = y_dest/distanceparam;
z = 1.0 - (x * x / 16.0) - (y * y / 4.0);
if(z<0)
{
*x_src=0;
*y_src=0;
return 0;
};
z = sqrt(z);
*x_src = 2.0 * atan2(z*x, 2.0*(2.0*z*z-1.0));
*y_src = asin(y*z);
if(fabs(*x_src) > PI || fabs(*y_src) > HALF_PI)
{
*x_src=0;
*y_src=0;
return 0;
};
*x_src *= distanceparam;
*y_src *= distanceparam;
return 1;
}
/** convert from erect to mercator FORWARD */
int mercator_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: distanceparam
*x_src = x_dest;
*y_src = distanceparam*log(tan(y_dest/distanceparam)+1/cos(y_dest/distanceparam));
return 1;
}
/** convert from mercator to erect INVERSE */
int erect_mercator( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: distanceparam
*x_src = x_dest;
*y_src = distanceparam*atan(sinh(y_dest/distanceparam));
return 1;
}
/** convert from erect to miller */
int millercylindrical_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: distanceparam
double phi, tanPhi;
*x_src = x_dest;
phi = y_dest/distanceparam;
tanPhi = tan(PI/4 +0.4 * phi);
if (tanPhi < 0) {
*x_src = 0;
*y_src = 0;
return 0;
};
*y_src = distanceparam*log(tanPhi)/0.8;
return 1;
}
/** convert from erect to miller */
int arch_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: distanceparam
if (y_dest < 0) {
return millercylindrical_erect(x_dest, y_dest, x_src, y_src, params);
} else {
return lambert_erect(x_dest, y_dest, x_src, y_src, params);
}
}
/** convert from erect to miller */
int erect_arch( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: distanceparam
if (y_dest < 0) {
return erect_millercylindrical(x_dest, y_dest, x_src, y_src, params);
} else {
return erect_lambert(x_dest, y_dest, x_src, y_src, params);
}
}
/** convert from miller cylindrical to erect */
int erect_millercylindrical( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
double y;
*x_src = x_dest;
y = y_dest/distanceparam;
y = 1.25 * atan(sinh(4 * y /5.0));
if ( fabs(y) > HALF_PI) {
*x_src = 0;
*y_src = 0;
return 0;
};
*y_src = distanceparam * y;
return 1;
}