shell.asy

import graph3;

size(10cm,0);
currentprojection=perspective(0,100,0);

real h_0 = 0.357;
real h_1 = 0.956;
real w_0 = 0.7;
real w_1  = 0.547;
real t_0 = 0.367;
real t_1 = 0.965;
real worls = 6.5;

triple e(triple v, real r, real beta) {
	return cos(beta) * v + (0,0,sin(beta) * r);
}

real f(real a, real b, real alpha) {
	return a*(1+b)^(alpha/(2pi));
}

typedef  real RtoR(real);
typedef  triple RtoR3(real);

RtoR3 xy(RtoR f) {
	return new triple(real p) {	return (cos(p),-sin(p),0)*f(p);	};
}

triple s(RtoR h, RtoR3 v, RtoR t, real alpha, real beta) {
	return (0,0,h(alpha)) + e(v(alpha),t(alpha),beta);
}

RtoR l_f(real a, real b, real m=1) {
	return new real(real alpha) {return f(a,b,alpha)*m;};
}

RtoR l_h() { return l_f(h_0,h_1,-1);}

RtoR3 l_v() { return xy(l_f(w_0,w_1));}

RtoR l_t() { return l_f(t_0,t_1,0.5);}

triple shell(pair t) {
  return s(l_h(),l_v(),l_t(),t.x,t.y);
}

surface s=surface(shell,(0.01,-pi/2),(2pi*worls,pi/2),50,8,Spline);
draw(s,rgb(0.6,0.6,0.7));