cal/cal/sphsamp.cal

{ RCSid $Id: sphsamp.cal,v 1.2 2005/02/15 23:36:10 greg Exp $ }
{
        Jittered sampling of a 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 (0-PI)
                phi_un  - azimuthal angle (unnormalized)
                phi     - azimuthal angle (0-2*PI)
                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 }

mod(n,d) : n - floor(n/d)*d;

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

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

sint = sin(theta);
Dx = cos(phi)*sint;
Dy = sin(phi)*sint;
Dz = cos(theta);
Revision:	1.3
Committed:	Tue Feb 15 23:45:14 2005 UTC (19 years, 2 months ago) by greg
Branch:	MAIN
CVS Tags:	rad5R4, rad5R2, rad4R2P2, rad5R0, rad5R1, rad3R7P2, rad3R7P1, rad4R2, rad4R1, rad4R0, rad3R8, rad3R9, rad4R2P1, rad5R3, HEAD
Changes since 1.2:	+10 -5 lines
Log Message:	Added normalization of azimuthal angle to (0-2*PI) range
#	User	Rev	Content
1	greg	1.3	{ RCSid $Id: sphsamp.cal,v 1.2 2005/02/15 23:36:10 greg Exp $ }
2	greg	1.1	{
3	greg	1.3	Jittered sampling of a sphere
4
5	greg	1.2	2/15/2005 G. Ward
6	greg	1.1
7	greg	1.2	Constant:
8			N - total number of samples on sphere
9			Input:
10			i - sample number [0,N-1]
11	greg	1.1	Output:
12	greg	1.3	theta - polar angle (0-PI)
13			phi_un - azimuthal angle (unnormalized)
14			phi - azimuthal angle (0-2*PI)
15	greg	1.1	Dx - X-component of direction vector
16			Dy - Y-component of direction vector
17			Dz - Z-component of direction vector
18			}
19	greg	1.2	S : .7; { jitter amount (0-1) }
20	greg	1.1
21	greg	1.2	k : 2*sqrt(PI/N); { k^2 is solid angle of each sample }
22	greg	1.1
23	greg	1.3	mod(n,d) : n - floor(n/d)*d;
24
25	greg	1.2	alpha0 = asin(2/N*(i+.5) - 1);
26	greg	1.1
27	greg	1.2	theta = alpha0 + PI/2 + kS(rand(.35*i+10.3) - .5);
28	greg	1.3	phi_un = sqrt(PIN)alpha0 + kS(rand(-.83*i-17.9) - .5);
29			phi = mod(phi_un, 2*PI);
30	greg	1.1
31	greg	1.2	sint = sin(theta);
32			Dx = cos(phi)*sint;
33			Dy = sin(phi)*sint;
34			Dz = cos(theta);