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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
#ifndef abs
#define abs(a) ( (a) >= 0 ? (a) : -(a) )
#endif
void matrix_matrix_mult ( double m1[3][3],double m2[3][3],double result[3][3]);
int polzeros_();
//------------------------- Some auxilliary math functions --------------------------------------------
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 distance (*((double*)params))
#define shift (*((double*)params))
#define var0 ((double*)params)[0]
#define var1 ((double*)params)[1]
// 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++;
}
}
// Rotate equirectangular image
void 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 ;
}
// Calculate inverse 4th order polynomial correction using Newton
// Don't use on large image (slow)!
void 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 ;
}
void 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 ;
}
void 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;
}
void 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;
}
void 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;
}
void 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;
}
void 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 ;
}
void 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 ;
}
void 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 ;
}
void persp_sphere( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params : double Matrix[3][3], double distance
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];
}
void persp_rect( double x_dest, double y_dest, double* x_src, double* y_src, void* params)
{
// params : double Matrix[3][3], double distance, 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] ;
}
void rect_pano( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
*x_src = distance * tan( x_dest / distance ) ;
*y_src = y_dest / cos( x_dest / distance );
}
void pano_rect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
*x_src = distance * atan ( x_dest / distance );
*y_src = y_dest * cos( *x_src / distance );
}
void rect_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance
register double phi, theta;
phi = x_dest / distance;
theta = - y_dest / distance + 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 = distance * tan(phi);
*y_src = distance / (tan( theta ) * cos(phi));
#endif
}
void pano_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance
*x_src = x_dest;
*y_src = distance * tan( y_dest / distance);
}
void erect_pano( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance
*x_src = x_dest;
*y_src = distance * atan( y_dest / distance);
}
void sphere_cp_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance, 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 );
}
void sphere_tp_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance
register double phi, theta, r,s;
double v[3];
phi = x_dest / distance;
theta = - y_dest / distance + 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 = distance * atan2( r , s * cos( phi ) );
*x_src = theta * v[0] / r;
*y_src = theta * v[1] / r;
}
void erect_sphere_cp( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance, 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;
}
void rect_sphere_tp( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance
register double rho, theta,r;
#if 0
theta = sqrt( x_dest * x_dest + y_dest * y_dest ) / distance;
phi = atan2( y_dest , x_dest );
if( theta > PI /2.0 || theta < -PI /2.0 )
theta = PI /2.0 ;
rho = distance * 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 / distance;
if( theta > PI /2.0 )
theta = PI /2.0 ;
if( theta == 0.0 )
rho = 1.0;
else
rho = tan( theta ) / theta;
*x_src = rho * x_dest ;
*y_src = rho * y_dest ;
}
void sphere_tp_rect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance
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) / distance;
if( r== 0.0 )
theta = 1.0;
else
theta = atan( r ) / r;
*x_src = theta * x_dest ;
*y_src = theta * y_dest ;
}
void sphere_tp_pano( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance
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 / distance );
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 / distance;
s = distance * sin( Phi ) ; // y' -> x
r = sqrt( s*s + y_dest*y_dest );
theta = distance * atan2( r , (distance * cos( Phi )) ) / r;
*x_src = theta * s ;
*y_src = theta * y_dest ;
#endif
}
void pano_sphere_tp( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance
register double r,s, theta;
double v[3];
#if 0
theta = sqrt( x_dest * x_dest + y_dest * y_dest ) / distance;
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 / distance;
if( theta == 0.0 )
s = 1.0 / distance;
else
s = sin( theta ) /r;
v[1] = s * x_dest ; // x' -> y
v[0] = cos( theta ); // z' -> x
*x_src = distance * atan2( v[1], v[0] );
*y_src = distance * s * y_dest / sqrt( v[0]*v[0] + v[1]*v[1] );
}
void sphere_cp_pano( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance
register double phi, theta;
phi = -x_dest / (distance * PI / 2.0) ;
theta = PI /2.0 + atan( y_dest / (distance * PI/2.0) );
*x_src = distance * theta * cos( phi );
*y_src = distance * theta * sin( phi );
}
void erect_rect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance
#if 0
theta = atan( sqrt(x_dest*x_dest + y_dest*y_dest) / distance );
phi = atan2( y_dest , x_dest );
v[1] = distance * sin( theta ) * cos( phi ); // x' -> y
v[2] = distance * sin( theta ) * sin( phi ); // y' -> z
v[0] = distance * 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 = distance * phi;
*y_src = distance * (-theta + PI /2.0);
#endif
*x_src = distance * atan2( x_dest, distance );
*y_src = distance * atan2( y_dest, sqrt( distance*distance + x_dest*x_dest ) );
}
void erect_sphere_tp( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance
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 / distance;
if(theta == 0.0)
s = 1.0 / distance;
else
s = sin( theta) / r;
v[1] = s * x_dest;
v[0] = cos( theta );
*x_src = distance * atan2( v[1], v[0] );
*y_src = distance * atan( s * y_dest /sqrt( v[0]*v[0] + v[1]*v[1] ) );
}
void mirror_sphere_cp( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance, 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 );
}
void mirror_erect( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance, 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 );
}
void mirror_pano( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance, 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 );
}
void sphere_cp_mirror( double x_dest,double y_dest, double* x_src, double* y_src, void* params)
{
// params: double distance, 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 );
}
void 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];
}
// 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;
}