{ RCSid $Id: vwparab.cal,v 1.2 2008/02/24 23:04:44 greg Exp $ }
{
	Generate rays for a parabolic view projection --
	i.e., a round image that when projected downwards
	in parallel onto a parabolic reflector results in
	a panoramic view from the paraboloid's focal point.

	The forward view direction corresponding to the top
	of the image is always +Y, and the up direction is
	always +Z.

	9/8/98 Greg Ward Larson

	Inputs:
		maxalt		: Maximum altitude (in degrees)
		x, y		= Image position, (0,0)->(1,0) is LL->LR

	Outputs:
		dx, dy, dz	= Direction vector for image point (x,y)

	Typical command line:
		cnt 1024 1024 | rcalc -od -e maxalt:25 \
			-e 'x=($2+.5)/1024;y=1-($1+.5)/1024' -f vwparab.cal \
			-e '$1=25.5;$2=12;$3=5;$4=dx;$5=dy;$6=dz' \
			| rtrace @electric.opt -fdc -x 1024 -y 1024 \
				electric.oct > pan.pic
}
amax : PI/180*maxalt;
F0 : .5/cos(amax) - .5*tan(amax);	{ dist. btwn. parabola and directrix }
xr = 2*x - 1;
yr = 2*y - 1;
r2 = xr*xr + yr*yr;
r = sqrt(r2);		{ never actually needed }
z = r2/(4*F0) + F0;
zo = r2/(4*F0) - F0;
sin_alt = zo/z;
cos_alt = r/z;
dx = xr/z;		{ same as xr/r*cos_alt }
dy = yr/z;		{ same as yr/r*cos_alt }
dz = zo/z;		{ same as sin_alt }