[PD] zexy 1.1 bugfix (was: cart2sph)

[Robert Figura]

On 21 Nov, bbogart at ryerson.ca wrote:

> I'm very confused by the values given by cart2sph in
> zexy 1.1. They conflict with my original expr based
> equation.
> 
> So If I have x=5, y=5 and z=5
[...]
> I'm using this equation:
>
> x^2+y^2+z^2=r^2
> theta=cos^-1(z/r)
> phi=tan^-1(y/x)
> 
>>From the zexy source I see:
> 
>   x->new_coord[0]=sqrtf(X*X+Y*Y+Z*Z);       /* R     */
>   x->new_coord[1]=atan2f(Y, X);             /* PHI   */
>   x->new_coord[2]=atan2f(Z, sqrt(X*X+Y*Y)); /* THETA */

PHI is all right, but if:
  atan2f(a,b) := atan(a/b)
then THETA is wrong (wrong parameter order), corrected:

$ diff zexy/src/z_coordinates.c ./z_coordinates.c
218c218
<   x->new_coord[2]=atan2f(Z, sqrt(X*X+Y*Y)); /* THETA */
---
>   x->new_coord[2]=atan2f(sqrt(X*X+Y*Y), Z); /* THETA */

Because of this identity:
  atan( sqrt( x*x + y*y ) / z ) == acos( z / r ).
Your formula also is correct. Lets see what my calculator says:

$ echo 'a( 5 / 5 )' | bc -l
.78539816339744830961

echo 'a( sqrt( 5*5 + 5*5 ) / 5 )' | bc -l 
.95531661812450927816

As to be expected. Any veto?

IOhannes? zexy 1.2? Or is it free on CVS? (ask first ;^)

BTW: atan2(a,b) is a standard c function? Makes sense in case b is zero.
     So i had had no need to implement it myself?

HTH
- Robert Figura

-- 
/* mandlsig.c v0.23  (c) by Robert Figura <rfigura at metabit.com> */
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