I have an equation for spherical sinusoid:
$$r=a$$
$$tan (\phi) = k*cos(n*\theta)$$
And the cartesian parametrization goes:
$$x=a*cos(t)/sqrt{(1 + k^2*cos^2(n*t))}$$
$$y=a*sin(t)/sqrt{(1 + k^2*cos^2(n*t))}$$
$$z=a*k*cos(n*t)/sqrt{(1 + k^2*cos^2(n*t))}$$
I have tried to reproduce the transformation with no luck. By solving $\phi$, Matlab with syms variables gives me
$$cos(atan(k*cos(n*th))) = 1//sqrt{(1 + k^2*cos^2(n*t))}$$
but still the equations dont add up.... Could someone give me a heads up please!?
Thanks in advance!