{ RCSid $Id: superellipsoid.cal,v 1.1 2013/12/07 01:56:28 greg Exp $ }
{
	Calculate superellipsoid surface
	using parametric formulation taken
	from Wikipedia

	12/6/2013	G. Ward

	Input parameters:
		A	- Radius in X-direction
		B	- Radius in Y-direction
		C	- Radius in Z-direction
		e	- 2/r parameter
		n	- 2/t parameter

	Example:
		gensurf mat name 'x(s,t)' 'y(s,t)' 'z(s,t)' 50 50 \
			-e 'A:1;B:1.5;C:2;e:.5;n:.7' -f superellipsoid.cal
}
ap(x,m) : if(x, x^m, if(-x, -(-x^m), 0));
fc(w,m) : ap(cos(w),m);
fs(w,m) : ap(sin(w),m);

x(s,t) = A * fc(t*PI-PI/2, n) * fc(s*2*PI-PI, e);
y(s,t) = B * fc(t*PI-PI/2, n) * fs(s*2*PI-PI, e);
z(s,t) = C * fs(t*PI-PI/2, n);