didi bruckmayr

has anyone taken a look at the spherical harmonics at:

http://astronomy.swin.edu.au/~pbourke/surfaces/sphericalh/

has anyone written an expression for this "simple formula"?

i constantly fuck up. my state of mind visible at

spherical-harmonics

On Jun 14, 2006, at 1:50 AM, didi bruckmayr wrote:

> has anyone taken a look at the spherical harmonics at:

> has anyone written an expression for this "simple formula"?

XYZ Eval(double theta,double phi, int *m)

is probably easiest to accomplish with two cascaded expressions. One 

to compute radius, r, and then passed to a second one to convert to 

In the above, replace m[N] with in[N] (to create adjustable 

parameters); replace theta with norm[0]*TWOPI, and phi with norm[1] 

*PI (to convert our normalized X and Y axis values to normalized 

radian based coordinates across the surface of the sphere), and that 

"pow(in[0]*PI*norm[1],in[1]) + pow(cos(in[2]*PI*norm[1]),in[3]) + 

pow(sin(in[4]*TWOPI*norm[0]),in[5]) + pow(cos(in[6]*TWOPI*norm[0]), 

then your output expressions for xyz would be the following (where 

theta and phi are replaced by the same, and r is replaced by in[0]). 

You could do with a single instance of jit.expr by replacing r with 

the first expression above, but it will be more expensive to compute 

for each x, y, and z rather than once for all, as I've suggested.

"in[0]*sin(PI*norm[1])*cos(TWOPI*norm[0])"

"in[0]*sin(PI*norm[1])*sin(TWOPI*norm[0])"

Quick hack example below. There's some stupid problem with updating 

the float values and jit.expr, which requires banging the input 

again, which I'll look into (might be some bug for jit.expr float 

input), but this should give a decent example of how to convert such 

>
> has anyone taken a look at the spherical harmonics at:
> http://astronomy.swin.edu.au/~pbourke/surfaces/sphericalh/
> has anyone written an expression for this "simple formula"?

XYZ Eval(double theta,double phi, int *m)
{
    double r = 0;
    XYZ p;

    r += pow(sin(m[0]*phi),(double)m[1]);
    r += pow(cos(m[2]*phi),(double)m[3]);
    r += pow(sin(m[4]*theta),(double)m[5]);
    r += pow(cos(m[6]*theta),(double)m[7]);

    p.x = r * sin(phi) * cos(theta);
    p.y = r * cos(phi);
    p.z = r * sin(phi) * sin(theta);

is probably easiest to accomplish with two cascaded expressions. One  
to compute radius, r, and then passed to a second one to convert to  
xyz based on r, theta, and phi.

In the above, replace m[N] with in[N] (to create adjustable  
parameters); replace theta with norm[0]*TWOPI, and phi with  norm[1] 
*PI (to convert our normalized X and Y axis values to normalized  
radian based coordinates across the surface of the sphere), and that  
should be it.

"pow(in[0]*PI*norm[1],in[1]) + pow(cos(in[2]*PI*norm[1]),in[3]) +  
pow(sin(in[4]*TWOPI*norm[0]),in[5]) +  pow(cos(in[6]*TWOPI*norm[0]), 
[7])"

then your output expressions for xyz would be the following (where  
theta and phi are replaced by the same, and r is replaced by in[0]).  
You could do with a single instance of jit.expr by replacing r with  
the first expression above, but it will be more expensive to compute  
for each x, y, and z rather than once for all, as I've suggested.

"in[0]*sin(PI*norm[1])*cos(TWOPI*norm[0])"
"in[0]*cos(PI*norm[1])"
"in[0]*sin(PI*norm[1])*sin(TWOPI*norm[0])"

Quick hack example below. There's some stupid problem with updating  
the float values and jit.expr, which requires banging the input  
again, which I'll look into (might be some bug for jit.expr float  
input), but this should give a decent example of how to convert such  
stuff into jit.expr expressions.