{ RCSid $Id: tregenza.cal,v 1.4 2009/09/15 00:17:36 greg Exp $ }
{
	Compute bin numbers corresponding to Tregenza sky discretization

	The Tregenza sky uses 145 patches, with patch 1 pointing due
	North at the horizon, and continuing around to the East to
	patch 30, which comprises the first altitude row (alt = 6 degrees).
	Each successive row increases altitude by 12 degrees, with the
	final altitude at the zenith (90 degrees).  Azimuth is evenly
	divided among 30, 30, 24, 24, 18, 12, 6, and 1 divisions per row.

	In addition to the bin numbers 1-145 corresponding to this
	standard, bin 0 is used for the ground plane (altitude < 0).

	Input is normalized ray direction (Dx,Dy,Dz).  The Y-axis is
	assumed to point North, and the X-axis East, matching the
	convention set by gensky(1).

	Greg Ward	May 2005
}
DEGREE : PI/180;
Asin(x) : if(x-1, PI/2, if(-1-x, -PI/2, asin(x)));
posangle(a) : if(-a, a + 2*PI, a);
Atan2(y,x) : posangle(atan2(y,x));

alt = Asin(Dz)/DEGREE;
azi = Atan2(Dx,Dy)/DEGREE;

tazi(inc) = if(359.9999-.5*inc - azi, floor((azi+.5*inc)/inc), 0);

tbin = if(-alt, 0,
	select(floor(alt/12) + 1,
		1 + tazi(12),
		31 + tazi(12),
		61 + tazi(15),
		85 + tazi(15),
		109 + tazi(20),
		127 + tazi(30),
		139 + tazi(60),
		145
	) );

Ntbins : 146;		{ total number of bins }