PaniniGeneral.c

/* PaniniGeneral.c		15Jan2010 TKS

Copyright (c) 2010, Thomas K Sharpless
All rights reserved.

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This is the reference implementation of the General Pannini
Projection, an elaboration of the basic Pannini projection 
discovered by Bruno Postle and Thomas Sharpless in December 
2008 in paintings by Gian Paolo Pannini (1691-1765).

*/
#include "PaniniGeneral.h"

#include <math.h>

#define PI 3.1415926535897932384626433832795
#define D2R( x ) ((x) * PI / 180 )
#define R2D( x ) ((x) * 180 / PI )

int panini_general_toSphere	( double* lon, double* lat, 
							  double h,  double v, 
							  double d, double top, double bot
							 )
{ 
	double S, cl, q, t;

	if( d < 0 ) return 0;
	q = v < 0 ? top : bot;
	if( h == 0 ){
        *lon = 0;
		S = 1;
		cl = 1;
	} else {
	/* solve quadratic for cosine of azimuth angle */
        double k, kk, dd, del;
        k = fabs(h) / (d + 1);
        kk = k * k;
        dd = d * d;
        del = kk * kk * dd - (kk + 1) * (kk * dd - 1);
        if( del < 0 ) 
            return 0;
        cl = (-kk * d + sqrt( del )) / (kk + 1);
	/* use that to compute S, and angle */
        S = (d + cl)/(d + 1);
		*lon = atan2( S * h, cl );
    }
	*lat = atan(S * v);

  /* squeeze */
	if( q > 0 ){
	/* hard squeeze */
		t = atan( v * cl );
		t = q * (t - *lat);
		*lat += t;
	} else if( q < 0 ){
	/* soft squeeze version 2 */
		double cc = cos(0.92 * *lon) - 1;
		double ss = 2 * d / (d + 1);
		t = v / (1 + ss * q * cc );
		*lat = atan( S * t );
	}

	return 1;
}
int panini_general_toPlane	( double lon, double lat, 
							  double*  h,  double*  v, 
							  double d, double top, double bot
							 )
{
	double S, q, t;

	if( d < 0 ) return 0;

	S = (d + 1) / (d + cos(lon));
	*h = sin(lon) * S;
	*v = tan(lat) * S;
    
  /* squeeze */
	q = lat < 0 ? top : bot;
	if( q < 0 ){
	/* soft squeeze version 2 */
		double cc = cos(0.92 * lon) - 1;
		double ss = 2 * d / (d + 1);
		*v *= 1 + ss * q * cc;
	} else if( q > 0 ){
	/* hard squeeze */
		t = cos(lon);
		if( t > 0.01 ) 
			t = *v / t;
		*v += q * (t - *v);
	}


	return 1;
}

int panini_general_maxVAs	( double d, 
							  double maxProj,
							  double * maxView
							 )
{	double a, s;

	if( d < 0 ) return 0;

/* hFOV... */
  // theoretical max angle (infeasible for d < 1.1 or so)
	if( d > 1. )
		s =  -1/d;
	else 
		s = -d;  
	a = acos( s );
  // actual limit may be max projection angle...
	s = asin(d * sin(maxProj)) + maxProj ; 
	if( a > s ){	// clip to projection angle limit
		a = s;	
	} 
    maxView[0] = a;

/* vFOV... */
	maxView[1] = maxProj;

	return 1;
}