[84e395]: math.c Maximize Restore History

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/* Panorama_Tools - Generate, Edit and Convert Panoramic Images
Copyright (C) 1998,1999 - Helmut Dersch der@fh-furtwangen.de
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 program; if not, write to the Free Software
Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */
/*------------------------------------------------------------*/
#include "filter.h"
#include <float.h>
#include "f2c.h"
#define R_EPS 1.0e-6
#define MAXITER 100
#include <assert.h>
#ifndef abs
#define abs(a) ( (a) >= 0 ? (a) : -(a) )
#endif
#ifdef _MSC_VER
#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_();
//------------------------- Some auxilliary math functions --------------------------------------------
// atanh is not available on MSVC. Use the atanh routine from gsl
#ifdef _MSC_VER
#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 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 = rs / rd;
// 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 shear( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// params: double shear_horizontal, double shear_vertical;
*x_src = x_dest + var0 * y_dest;
*y_src = y_dest + var1 * x_dest;
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
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 mercator */
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 */
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 lambert */
int lambert_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: distanceparam
*x_src = x_dest;
*y_src = distanceparam*sin(y_dest/distanceparam);
return 1;
}
/** convert from lambert to erect */
int erect_lambert( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: distanceparam
*x_src = x_dest;
*y_src = distanceparam*asin(y_dest/distanceparam);
return 1;
}
/** convert from erect to transverse mercator */
int transmercator_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: distanceparam
double B;
x_dest /= distanceparam;
y_dest /= distanceparam;
B = cos(y_dest)*sin(x_dest);
*x_src = distanceparam * atanh(B);
*y_src = distanceparam * atan2(tan(y_dest), cos(x_dest));
if (isinf(*x_src)) {
return 0;
}
return 1;
}
/** convert from erect to transverse mercator */
int erect_transmercator( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: distanceparam
x_dest /= distanceparam;
y_dest /= distanceparam;
if (fabs(y_dest) > PI ) {
*y_src = 0;
*x_src = 0;
return 0;
}
*x_src = distanceparam * atan2(sinh(x_dest),cos(y_dest));
*y_src = distanceparam * asin(sin(y_dest)/cosh(x_dest));
return 1;
}
/** convert from erect to sinusoidal */
int sinusoidal_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: distanceparam
*x_src = distanceparam * (x_dest/distanceparam*cos(y_dest/distanceparam));
*y_src = y_dest;
return 1;
}
/** convert from sinusoidal to erect */
int erect_sinusoidal( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: distanceparam
*y_src = y_dest;
*x_src = x_dest/cos(y_dest/distanceparam);
if (*x_src/distanceparam < -PI || *x_src/distanceparam > PI)
return 0;
return 1;
}
/** convert from erect to stereographic */
int stereographic_erect_old( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: distanceparam
double lon = x_dest / distanceparam;
double lat = y_dest / distanceparam;
// use: R = 1
double k=2.0/(1+cos(lat)*cos(lon));
*x_src = distanceparam * k*cos(lat)*sin(lon);
*y_src = distanceparam * k*sin(lat);
return 1;
}
int stereographic_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
double lon, lat;
double sinphi, cosphi, coslon;
double g,ksp;
lon = x_dest / distanceparam;
lat = y_dest / distanceparam;
sinphi = sin(lat);
cosphi = cos(lat);
coslon = cos(lon);
g = cosphi * coslon;
// point projects to infinity:
// if (fabs(g + 1.0) <= EPSLN)
ksp = distanceparam * 2.0 / (1.0 + g);
*x_src = ksp * cosphi * sin(lon);
*y_src = ksp * sinphi;
return 1;
}
/** convert from stereographic to erect */
int erect_stereographic( double x_dest,double y_dest, double* lon, double* lat, void* params)
{
double rh; /* height above sphere*/
double c; /* angle */
double sinc,cosc; /* sin of c and cos of c */
double con;
/* Inverse equations
-----------------*/
double x = x_dest / distanceparam;
double y = y_dest / distanceparam;
rh = sqrt(x * x + y * y);
c = 2.0 * atan(rh / (2.0 * 1));
sinc = sin(c);
cosc = cos(c);
*lon = 0;
if (fabs(rh) <= EPSLN)
{
*lat = 0;
return 0;
}
else
{
*lat = asin((y * sinc) / rh) * distanceparam;
con = HALF_PI;
con = cosc;
if ((fabs(cosc) < EPSLN) && (fabs(x) < EPSLN))
return 0;
else
*lon = atan2((x * sinc), (cosc * rh)) * distanceparam;
}
return 1;
}
/** convert from stereographic to erect */
int erect_stereographic_old( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: distanceparam
// use: R = 1
double p=sqrt(x_dest*x_dest + y_dest*y_dest) / distanceparam;
double c= 2.0*atan(p/2.0);
*x_src = distanceparam * atan2(x_dest/distanceparam*sin(c),(p*cos(c)));
*y_src = distanceparam * asin(y_dest/distanceparam*sin(c)/p);
return 1;
}
int albersEqualAreaConic_ParamCheck(Image *im)
{
//Parameters: phi1, phi2, phi0, n, C, rho0, yoffset
double phi1, phi2, n, C, rho0, phi0, y1, y2, y, twiceN;
double phi[] = {-PI/2, 0, PI/2};
double lambda[] = {-PI, 0, PI};
int i, j, first;
assert(PANO_PROJECTION_MAX_PARMS >= 2);
if (im->formatParamCount == 1) {
// WHen only one parameter provided, assume phi1=phi0
im->formatParamCount = 2;
im->formatParam[1] = im->formatParam[0];
}
if (im->formatParamCount == 0) {
im->formatParamCount = 2;
im->formatParam[0] = 0; //phi1
im->formatParam[1] = -60; //phi2
}
if (im->precomputedCount == 0) {
im->precomputedCount = 10;
assert(PANO_PROJECTION_PRECOMPUTED_VALUES >=im->precomputedCount );
// First, invert standard parallels.
// This is a hack, as the resulting projections look backwards to what they are supposed to be
// (with respect to maps)
im->precomputedValue[0] = -1.0 * im->formatParam[0];
im->precomputedValue[1] = -1.0 * im->formatParam[1];
phi1 = im->precomputedValue[0] * PI / 180.0; //phi1 to rad
phi2 = im->precomputedValue[1] * PI / 180.0; //phi2 to rad
//Calculate the y at 6 different positions (lambda=-pi,0,+pi; phi=-pi/2,0,pi/2).
///Then calculate a yoffset so that the image is centered.
first = 1;
for (i = 0; i < 3; i++) for (j = 0; j < 3; j++) {
y = sqrt(pow(cos(phi1), 0.2e1) + 0.2e1 * (sin(phi1) / 0.2e1 + sin(phi2) / 0.2e1) * sin(phi1)) / (sin(phi1) / 0.2e1 + sin(phi2) / 0.2e1) - sqrt(pow(cos(phi1), 0.2e1) + 0.2e1 * (sin(phi1) / 0.2e1 + sin(phi2) / 0.2e1) * sin(phi1) - 0.2e1 * (sin(phi1) / 0.2e1 + sin(phi2) / 0.2e1) * sin(phi[i])) / (sin(phi1) / 0.2e1 + sin(phi2) / 0.2e1) * cos((sin(phi1) / 0.2e1 + sin(phi2) / 0.2e1) * lambda[j]);
if (!isnan(y)) {
if (first || y < y1) y1 = y;
if (first || y > y2) y2 = y;
first = 0;
}
}
if (first) {
y = 0;
} else {
y = y1 + fabs(y1 - y2)/2.0;
}
// The stability of these operations should be improved
phi0 = 0;
twiceN = sin(phi1) + sin(phi2);
n = twiceN /2.0;
C = cos(phi1) * cos(phi1) + 2.0 * n * sin(phi1);
rho0 = sqrt(C - 2.0 * n * sin(phi0)) / n;
im->precomputedValue[0] = phi1;
im->precomputedValue[1] = phi2;
im->precomputedValue[2] = phi0;
im->precomputedValue[3] = n;
im->precomputedValue[4] = C;
im->precomputedValue[5] = rho0;
im->precomputedValue[6] = y;
im->precomputedValue[7] = n*n;
im->precomputedValue[8] = sin(phi1) + sin(phi2);
im->precomputedValue[9] = twiceN;
// printf("Parms phi1 %f phi2 %f pho0 %f, n %f, C %f, rho0 %f, %f\n",
// phi1, phi2, phi0, n, C, rho0, y);
}
for (i=0;i<im->precomputedCount;i++) {
assert(!isnan(im->precomputedValue[i]));
}
if (im->precomputedCount > 0) return 1;
// PrintError("false in alberts equal area parameters");
return 0;
}
/** convert from erect to albersequalareaconic */
int albersequalareaconic_erect( double x_dest,double y_dest, double* x_src, double* y_src, void *params)
{
double yoffset, lambda, phi, lambda0, n, C, rho0, theta, rho;
double twiceN;
// Forward calculation
if (!albersEqualAreaConic_ParamCheck(mp->pn)) {
// printf("REturning abert->erect 0\n");
return 0;
}
assert(!isnan(x_dest));
assert(!isnan(y_dest));
lambda = x_dest / mp->distance;
phi = y_dest / mp->distance;
if (lambda > PI) lambda-=2*PI;
if (lambda < -PI) lambda+=2*PI;
lambda0 = 0;
n = mp->pn->precomputedValue[3];
C = mp->pn->precomputedValue[4];
rho0 = mp->pn->precomputedValue[5];
yoffset = mp->pn->precomputedValue[6];
twiceN = mp->pn->precomputedValue[9];
theta = n * (lambda - lambda0);
// printf("value %f\n", (phi));
// printf("value %f\n", sin(phi));
// printf("value %f\n", C - 2.0 * n * sin(phi));
//assert(C - 2.0 * n * sin(phi) >=0);
rho = sqrt(C - twiceN * sin(phi)) / n;
*x_src = mp->distance * (rho * sin(theta));
*y_src = mp->distance * (rho0 - rho * cos(theta) - yoffset);
if (isnan(*x_src) ||
isnan(*y_src)) {
*x_src = 0;
*y_src = 0;
// PrintError("false in alberts equal area 4");
return 0;
}
assert(!isnan(*x_src));
assert(!isnan(*y_src));
return 1;
}
/** convert from albersequalareaconic to erect */
int erect_albersequalareaconic(double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
double x, y, yoffset, lambda0, n, C, rho0, theta, phi, lambda, nsign;
double rho2; // rho^2
double n2; // n^2
double twiceN; // n * 2.0
// Inverse calculation
if (!albersEqualAreaConic_ParamCheck(mp->pn)) {
*x_src = 0;
*y_src = 0;
// printf("false in alberts equal area\n");
return 0;
}
x = x_dest / mp->distance;
y = y_dest / mp->distance;
lambda0 = 0;
n = mp->pn->precomputedValue[3];
C = mp->pn->precomputedValue[4];
rho0 = mp->pn->precomputedValue[5];
yoffset = mp->pn->precomputedValue[6];
n2 = mp->pn->precomputedValue[7];
twiceN = mp->pn->precomputedValue[9];
y = y + yoffset;
rho2 = x*x + (rho0 - y)*(rho0 - y);
nsign = 1.0;
if (n < 0) nsign = -1.0;
theta = atan2(nsign * x, nsign * (rho0 - y));
phi = asin((C - rho2 * n2)/twiceN);
lambda = lambda0 + theta / n;
if (lambda > PI || lambda < -PI) {
*x_src = 0;
*y_src = 0;
// PrintError("false in alberts equal area 2");
return 0;
}
*x_src = mp->distance * lambda;
*y_src = mp->distance * phi;
if (isnan(*x_src) ||
isnan(*y_src)) {
*x_src = 0;
*y_src = 0;
// PrintError("false in alberts equal area 3");
return 0;
}
assert(!isnan(*x_src));
assert(!isnan(*y_src));
return 1;
}
int albersequalareaconic_distance(double* x_src, void* params) {
double x1, x2, y, phi1, phi2, lambda;
// printf("alber distance\n");
if (!albersEqualAreaConic_ParamCheck(mp->pn)) {
*x_src = 0;
// printf("false in alberts equal area distance 0\n");
return 0;
}
mp->distance = 1;
phi1 = mp->pn->precomputedValue[0];
phi2 = mp->pn->precomputedValue[1];
//lambda where x is a maximum.
if (phi1 == phi2 &&
phi1 == 0.0) {
// THIS IS A HACK...it needs to further studied
// why this when phi1==phi2==0
// this functions return 0
// Avoid approximation error
PrintError("The Albers projection cannot be used for phi1==phi2==0. Use Lambert Cylindrical Equal Area instead");
*x_src = PI;
return 0;
}
lambda = fabs(PI / (sin(phi1) + sin(phi2)));
if (lambda > PI) lambda = PI;
albersequalareaconic_erect(lambda, -PI/2.0, &x1, &y, mp);
albersequalareaconic_erect(lambda, PI/2.0, &x2, &y, mp);
*x_src = max(fabs(x1), fabs(x2));
if (isnan(*x_src)) {
*x_src = 0;
PrintError("false in alberts equal area distance 1");
return 0;
}
assert(!isnan(*x_src));
// printf("return albers distance %f\n", *x_src);
return 1;
}
int sphere_cp_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam, double b
register double phi, theta;
#if 0
phi = - x_dest / ( var0 * PI / 2.0);
theta = - ( y_dest + var1 ) / (var0 * PI / 2.0) ;
*x_src = var0 * theta * cos( phi );
*y_src = var0 * theta * sin( phi );
#endif
phi = - x_dest / ( var0 * PI / 2.0);
theta = - ( y_dest + var1 ) / ( PI / 2.0) ;
*x_src = theta * cos( phi );
*y_src = theta * sin( phi );
return 1;
}
int sphere_tp_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam
register double phi, theta, r,s;
double v[3];
phi = x_dest / distanceparam;
theta = - y_dest / distanceparam + PI / 2;
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
theta = atan2( sqrt( v[0]*v[0] + v[1]*v[1] ) , v[2] );
phi = atan2( v[1], v[0] );
*x_src = *((double*)params) * theta * cos( phi );
*y_src = *((double*)params) * theta * sin( phi );
#endif
s = sin( theta );
v[0] = s * sin( phi ); // y' -> x
v[1] = cos( theta ); // z' -> y
r = sqrt( v[1]*v[1] + v[0]*v[0]);
theta = distanceparam * atan2( r , s * cos( phi ) );
*x_src = theta * v[0] / r;
*y_src = theta * v[1] / r;
return 1;
}
int erect_sphere_cp( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam, double b
register double phi, theta;
#if 0
theta = sqrt( x_dest * x_dest + y_dest * y_dest ) / var0;
phi = atan2( y_dest , -x_dest );
*x_src = var0 * phi;
*y_src = var0 * theta - var1;
#endif
theta = sqrt( x_dest * x_dest + y_dest * y_dest ) ;
phi = atan2( y_dest , -x_dest );
*x_src = var0 * phi;
*y_src = theta - var1;
return 1;
}
int rect_sphere_tp( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam
register double rho, theta,r;
#if 0
theta = sqrt( x_dest * x_dest + y_dest * y_dest ) / distanceparam;
phi = atan2( y_dest , x_dest );
if( theta > PI /2.0 || theta < -PI /2.0 )
theta = PI /2.0 ;
rho = distanceparam * tan( theta );
*x_src = rho * cos( phi );
*y_src = rho * sin( phi );
#endif
r = sqrt( x_dest * x_dest + y_dest * y_dest );
theta = r / distanceparam;
if( theta >= PI /2.0 )
rho = 1.6e16 ;
else if( theta == 0.0 )
rho = 1.0;
else
rho = tan( theta ) / theta;
*x_src = rho * x_dest ;
*y_src = rho * y_dest ;
return 1;
}
int sphere_tp_rect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam
register double theta, r;
#if 0
theta = atan( sqrt(x_dest*x_dest + y_dest*y_dest) / *((double*)params));
phi = atan2( y_dest , x_dest );
*x_src = *((double*)params) * theta * cos( phi );
*y_src = *((double*)params) * theta * sin( phi );
#endif
r = sqrt(x_dest*x_dest + y_dest*y_dest) / distanceparam;
if( r== 0.0 )
theta = 1.0;
else
theta = atan( r ) / r;
*x_src = theta * x_dest ;
*y_src = theta * y_dest ;
return 1;
}
int sphere_tp_pano( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam
register double r, s, Phi, theta;
#if 0
register double Theta, phi;
double v[3];
Phi = x_dest / *((double*)params);
Theta = PI /2.0 - atan( y_dest / distanceparam );
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
theta = atan2( sqrt( v[0]*v[0] + v[1]*v[1] ) , v[2] );
phi = atan2( v[1], v[0] );
*x_src = *((double*)params) * theta * cos( phi );
*y_src = *((double*)params) * theta * sin( phi );
#endif
#if 1
Phi = x_dest / distanceparam;
s = distanceparam * sin( Phi ) ; // y' -> x
r = sqrt( s*s + y_dest*y_dest );
theta = distanceparam * atan2( r , (distanceparam * cos( Phi )) ) / r;
*x_src = theta * s ;
*y_src = theta * y_dest ;
#endif
return 1;
}
int pano_sphere_tp( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam
register double r,s, theta;
double v[3];
#if 0
theta = sqrt( x_dest * x_dest + y_dest * y_dest ) / distanceparam;
phi = atan2( y_dest , x_dest );
v[1] = *((double*)params) * sin( theta ) * cos( phi ); // x' -> y
v[2] = *((double*)params) * sin( theta ) * sin( phi ); // y' -> z
v[0] = *((double*)params) * cos( theta ); // z' -> x
theta = atan2( sqrt( v[0]*v[0] + v[1]*v[1] ) , v[2] );
phi = atan2( v[1], v[0] );
*x_src = *((double*)params) * phi;
*y_src = *((double*)params) * tan( (-theta + PI /2.0) );
#endif
r = sqrt( x_dest * x_dest + y_dest * y_dest );
theta = r / distanceparam;
if( theta == 0.0 )
s = 1.0 / distanceparam;
else
s = sin( theta ) /r;
v[1] = s * x_dest ; // x' -> y
v[0] = cos( theta ); // z' -> x
*x_src = distanceparam * atan2( v[1], v[0] );
*y_src = distanceparam * s * y_dest / sqrt( v[0]*v[0] + v[1]*v[1] );
return 1;
}
int sphere_cp_pano( 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 * PI / 2.0) ;
theta = PI /2.0 + atan( y_dest / (distanceparam * PI/2.0) );
*x_src = distanceparam * theta * cos( phi );
*y_src = distanceparam * theta * sin( phi );
return 1;
}
int erect_rect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam
#if 0
theta = atan( sqrt(x_dest*x_dest + y_dest*y_dest) / distanceparam );
phi = atan2( y_dest , x_dest );
v[1] = distanceparam * sin( theta ) * cos( phi ); // x' -> y
v[2] = distanceparam * sin( theta ) * sin( phi ); // y' -> z
v[0] = distanceparam * cos( theta ); // z' -> x
theta = atan2( sqrt( v[0]*v[0] + v[1]*v[1] ) , v[2] );
phi = atan2( v[1], v[0] );
*x_src = distanceparam * phi;
*y_src = distanceparam * (-theta + PI /2.0);
#endif
*x_src = distanceparam * atan2( x_dest, distanceparam );
*y_src = distanceparam * atan2( y_dest, sqrt( distanceparam*distanceparam + x_dest*x_dest ) );
return 1;
}
int erect_sphere_tp( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam
register double theta,r,s;
double v[3];
#if 0
theta = sqrt( x_dest * x_dest + y_dest * y_dest ) / *((double*)params);
phi = atan2( y_dest , x_dest );
v[1] = *((double*)params) * sin( theta ) * cos( phi ); // x' -> y
v[2] = *((double*)params) * sin( theta ) * sin( phi ); // y' -> z
v[0] = *((double*)params) * cos( theta ); // z' -> x
theta = atan( sqrt( v[0]*v[0] + v[1]*v[1] ) / v[2] ); //was atan2
phi = atan2( v[1], v[0] );
*x_src = *((double*)params) * phi;
if(theta > 0.0)
{
*y_src = *((double*)params) * (-theta + PI /2.0);
}
else
*y_src = *((double*)params) * (-theta - PI /2.0);
#endif
r = sqrt( x_dest * x_dest + y_dest * y_dest );
theta = r / distanceparam;
if(theta == 0.0)
s = 1.0 / distanceparam;
else
s = sin( theta) / r;
v[1] = s * x_dest;
v[0] = cos( theta );
*x_src = distanceparam * atan2( v[1], v[0] );
*y_src = distanceparam * atan( s * y_dest /sqrt( v[0]*v[0] + v[1]*v[1] ) );
return 1;
}
int mirror_sphere_cp( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam, double b
register double rho, phi, theta;
theta = sqrt( x_dest * x_dest + y_dest * y_dest ) / ((double*)params)[0];
phi = atan2( y_dest , x_dest );
rho = ((double*)params)[1] * sin( theta / 2.0 );
*x_src = - rho * cos( phi );
*y_src = rho * sin( phi );
return 1;
}
int mirror_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam, double b, double b2
register double phi, theta, rho;
phi = x_dest / ( ((double*)params)[0] * PI/2.0) ;
theta = - ( y_dest + ((double*)params)[2] ) / (((double*)params)[0] * PI/2.0) ;
rho = ((double*)params)[1] * sin( theta / 2.0 );
*x_src = - rho * cos( phi );
*y_src = rho * sin( phi );
return 1;
}
int mirror_pano( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam, double b
register double phi, theta, rho;
phi = -x_dest / (((double*)params)[0] * PI/2.0) ;
theta = PI /2.0 + atan( y_dest / (((double*)params)[0] * PI/2.0) );
rho = ((double*)params)[1] * sin( theta / 2.0 );
*x_src = rho * cos( phi );
*y_src = rho * sin( phi );
return 1;
}
int sphere_cp_mirror( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distanceparam, double b
register double phi, theta, rho;
rho = sqrt( x_dest*x_dest + y_dest*y_dest );
theta = 2 * asin( rho/((double*)params)[1] );
phi = atan2( y_dest , x_dest );
*x_src = ((double*)params)[0] * theta * cos( phi );
*y_src = ((double*)params)[0] * theta * sin( phi );
return 1;
}
int shift_scale_rotate( double x_dest,double y_dest, double* x_src, double* y_src, void* params){
// params: double shift_x, shift_y, scale, cos_phi, sin_phi
register double x = x_dest - ((double*)params)[0];
register double y = y_dest - ((double*)params)[1];
*x_src = (x * ((double*)params)[3] - y * ((double*)params)[4]) * ((double*)params)[2];
*y_src = (x * ((double*)params)[4] + y * ((double*)params)[3]) * ((double*)params)[2];
return 1;
}
// Correct radial luminance change using parabel
unsigned char radlum( unsigned char srcPixel, int xc, int yc, void *params )
{
// params: second and zero order polynomial coeff
register double result;
result = (xc * xc + yc * yc) * ((double*)params)[0] + ((double*)params)[1];
result = ((double)srcPixel) - result;
// JMW 2003/08/25 randomize a little
result = result * ( (1 + LUMINANCE_RANDOMIZE/2) - LUMINANCE_RANDOMIZE * rand() / (double)RAND_MAX );
if(result < 0.0) return 0;
if(result > 255.0) return 255;
return( (unsigned char)(result+0.5) );
}
//Kekus 16 bit: 2003/Nov/18
//Correct radial luminance change using parabel (16-bit supported)
unsigned short radlum16( unsigned short srcPixel, int xc, int yc, void *params )
{
// params: second and zero order polynomial coeff
register double result;
result = (xc * xc + yc * yc) * ((double*)params)[0] + ((double*)params)[1];
result = ((double) srcPixel) - result*256;
// JMW 2003/08/25 randomize a little to remove banding added by Kekus Digital 26 Aug 2003
// JMW 2004/07/11 a power of two less randomizing for 16 bit
result = result * ( (1 + LUMINANCE_RANDOMIZE * LUMINANCE_RANDOMIZE /2) -
LUMINANCE_RANDOMIZE * LUMINANCE_RANDOMIZE * rand() / (double)RAND_MAX );
if(result > 65535.0) return 65535;
if(result < 0.0) return 0;
return( (unsigned short)(result+0.5) );
}
//Kekus.
// Get smallest positive (non-zero) root of polynomial with degree deg and
// (n+1) real coefficients p[i]. Return it, or 1000.0 if none exists or error occured
// Changed to only allow degree 3
#if 0
double smallestRoot( double *p )
{
doublecomplex root[3], poly[4];
doublereal radius[3], apoly[4], apolyr[4];
logical myErr[3];
double sRoot = 1000.0;
doublereal theEps, theBig, theSmall;
integer nitmax;
integer iter;
integer n,i;
n = 3;
for( i=0; i< n+1; i++)
{
poly[i].r = p[i];
poly[i].i = 0.0;
}
theEps = DBL_EPSILON; // machine precision
theSmall = DBL_MIN ; // smallest positive real*8
theBig = DBL_MAX ; // largest real*8
nitmax = 100;
polzeros_(&n, poly, &theEps, &theBig, &theSmall, &nitmax, root, radius, myErr, &iter, apoly, apolyr);
for( i = 0; i < n; i++ )
{
// PrintError("No %d : Real %g, Imag %g, radius %g, myErr %ld", i, root[i].r, root[i].i, radius[i], myErr[i]);
if( (root[i].r > 0.0) && (dabs( root[i].i ) <= radius[i]) && (root[i].r < sRoot) )
sRoot = root[i].r;
}
return sRoot;
}
#endif
void cubeZero( double *a, int *n, double *root );
void squareZero( double *a, int *n, double *root );
double cubeRoot( double x );
void cubeZero( double *a, int *n, double *root ){
if( a[3] == 0.0 ){ // second order polynomial
squareZero( a, n, root );
}else{
double p = ((-1.0/3.0) * (a[2]/a[3]) * (a[2]/a[3]) + a[1]/a[3]) / 3.0;
double q = ((2.0/27.0) * (a[2]/a[3]) * (a[2]/a[3]) * (a[2]/a[3]) - (1.0/3.0) * (a[2]/a[3]) * (a[1]/a[3]) + a[0]/a[3]) / 2.0;
if( q*q + p*p*p >= 0.0 ){
*n = 1;
root[0] = cubeRoot(-q + sqrt(q*q + p*p*p)) + cubeRoot(-q - sqrt(q*q + p*p*p)) - a[2] / (3.0 * a[3]);
}else{
double phi = acos( -q / sqrt(-p*p*p) );
*n = 3;
root[0] = 2.0 * sqrt(-p) * cos(phi/3.0) - a[2] / (3.0 * a[3]);
root[1] = -2.0 * sqrt(-p) * cos(phi/3.0 + PI/3.0) - a[2] / (3.0 * a[3]);
root[2] = -2.0 * sqrt(-p) * cos(phi/3.0 - PI/3.0) - a[2] / (3.0 * a[3]);
}
}
// PrintError("%lg, %lg, %lg, %lg root = %lg", a[3], a[2], a[1], a[0], root[0]);
}
void squareZero( double *a, int *n, double *root ){
if( a[2] == 0.0 ){ // linear equation
if( a[1] == 0.0 ){ // constant
if( a[0] == 0.0 ){
*n = 1; root[0] = 0.0;
}else{
*n = 0;
}
}else{
*n = 1; root[0] = - a[0] / a[1];
}
}else{
if( 4.0 * a[2] * a[0] > a[1] * a[1] ){
*n = 0;
}else{
*n = 2;
root[0] = (- a[1] + sqrt( a[1] * a[1] - 4.0 * a[2] * a[0] )) / (2.0 * a[2]);
root[1] = (- a[1] - sqrt( a[1] * a[1] - 4.0 * a[2] * a[0] )) / (2.0 * a[2]);
}
}
}
double cubeRoot( double x ){
if( x == 0.0 )
return 0.0;
else if( x > 0.0 )
return pow(x, 1.0/3.0);
else
return - pow(-x, 1.0/3.0);
}
double smallestRoot( double *p ){
int n,i;
double root[3], sroot = 1000.0;
cubeZero( p, &n, root );
for( i=0; i<n; i++){
// PrintError("Root %d = %lg", i,root[i]);
if(root[i] > 0.0 && root[i] < sroot)
sroot = root[i];
}
// PrintError("Smallest Root = %lg", sroot);
return sroot;
}