cal/cal/sphsamp.cal

{ RCSid $Id$ }
{
        Uniform sampling of sphere
        2/15/2005       G. Ward

        Constant:
                N -             total number of samples on sphere
        Input:
                i -             sample number [0,N-1]
        Output:
                theta   - polar angle (radians)
                phi     - azimuthal angle (radians)
                Dx      - X-component of direction vector
                Dy      - Y-component of direction vector
                Dz      - Z-component of direction vector
}
S : .7;                 { jitter amount (0-1) }

k : 2*sqrt(PI/N);       { k^2 is solid angle of each sample }

alpha0 = asin(2/N*(i+.5) - 1);

theta = alpha0 + PI/2 + k*S*(rand(.35*i+10.3) - .5);
phi = sqrt(PI*N)*alpha0 + k*S*(rand(-.83*i-17.9) - .5);

sint = sin(theta);
Dx = cos(phi)*sint;
Dy = sin(phi)*sint;
Dz = cos(theta);
Revision:	1.2
Committed:	Tue Feb 15 23:36:10 2005 UTC (19 years, 2 months ago) by greg
Branch:	MAIN
Changes since 1.1:	+17 -27 lines
Log Message:	Improved sampling algorithm to be more uniform over sphere (degrees -> radians)
#	User	Rev	Content
1	greg	1.2	{ RCSid $Id$ }
2	greg	1.1	{
3			Uniform sampling of sphere
4	greg	1.2	2/15/2005 G. Ward
5	greg	1.1
6	greg	1.2	Constant:
7			N - total number of samples on sphere
8			Input:
9			i - sample number [0,N-1]
10	greg	1.1	Output:
11	greg	1.2	theta - polar angle (radians)
12			phi - azimuthal angle (radians)
13	greg	1.1	Dx - X-component of direction vector
14			Dy - Y-component of direction vector
15			Dz - Z-component of direction vector
16			}
17	greg	1.2	S : .7; { jitter amount (0-1) }
18	greg	1.1
19	greg	1.2	k : 2*sqrt(PI/N); { k^2 is solid angle of each sample }
20	greg	1.1
21	greg	1.2	alpha0 = asin(2/N*(i+.5) - 1);
22	greg	1.1
23	greg	1.2	theta = alpha0 + PI/2 + kS(rand(.35*i+10.3) - .5);
24			phi = sqrt(PIN)alpha0 + kS(rand(-.83*i-17.9) - .5);
25	greg	1.1
26	greg	1.2	sint = sin(theta);
27			Dx = cos(phi)*sint;
28			Dy = sin(phi)*sint;
29			Dz = cos(theta);