seashells_draft

l[{n_}, theta_] :=
  (2*Pi/n) ((n*theta/(2*Pi)) - IntegerPart[n*theta/(2*Pi)]);
k[{a_, b_, ll_, p_, w1_, w2_, n_}, s_, theta_] :=
  	If[w1 == 0 || w2 == 0 || n == 0,
   		0,
   		ll*Exp[-(2*(s - p)/w1)^2 - (2*l[{n}, theta]/w2)^2]
   		];
h[{a_, b_, ll_, p_, w1_, w2_, n_}, s_, theta_] :=
 	(1/(Sqrt[(Cos[s]/a)^2 + (Sin[s]/b)^2]))
		+k[{a, b, ll, p, w1, w2, n}, s, theta];

(*cartesian coordinates*)
x[{d_, aa_, beta_, phi_, omega_, mu_, alpha_, a_, b_, ll_, p_, w1_,
    w2_, n_}, theta_, s_] :=
  		d*(aa*Sin[beta]*Cos[theta]
     		+ h[{a, b, ll, p, w1, w2, n}, s,
       theta]*(Cos[s + phi]*Cos[theta + omega] -
        Sin[mu]*Sin[s + phi]*Sin[theta + omega]))*
   Exp[theta*Cot[alpha]];
y[{aa_, beta_, phi_, omega_, mu_, alpha_, a_, b_, ll_, p_, w1_, w2_,
    n_}, theta_, s_] :=
  (-aa*Sin[beta]*Sin[theta] -
     h[{a, b, ll, p, w1, w2, n}, s,
       theta]*(Cos[s + phi]*Sin[theta + omega] +
        Sin[mu]*Sin[s + phi]*Cos[theta + omega]))*
   Exp[theta*Cot[alpha]];
z[{aa_, beta_, phi_, mu_, alpha_, a_, b_, ll_, p_, w1_, w2_, n_},
   theta_, s_] :=
  	(-aa*Cos[beta] +
     h[{a, b, ll, p, w1, w2, n}, s, theta]*Sin[s + phi]*Cos[mu])*
   Exp[theta*Cot[alpha]];

(*sample*)
With[{d = 1, aa = 90, beta = 10 Degree, phi = 45 Degree,
  omega = 1 Degree, mu = 5 Degree, alpha = 86 Degree, a = 20, b = 20,
  ll = 14, p = 0, w1 = 180, w2 = .4, n = 180},
 ParametricPlot3D[{x[{d, aa, beta, phi, omega, mu, alpha, a, b, ll, p,
      w1, w2, n}, theta, s],
   y[{aa, beta, phi, omega, mu, alpha, a, b, ll, p, w1, w2, n}, theta,
     s],
   z[{aa, beta, phi, mu, alpha, a, b, ll, p, w1, w2, n}, theta, s]},
  	{theta, -10*Pi, 10*Pi},
  	{s, -270 Degree, 90 Degree},
  PlotRange -> All, PlotPoints -> 50, Mesh -> False, Boxed -> False,
  Axes -> False,
  PlotStyle -> {Darker[Orange, 0.1], Specularity[White, 20]},
  Background -> GrayLevel[0.5],
   SphericalRegion -> True,
  ViewPoint ->
   RotationTransform[-3 Pi/4, {0, 2, 1}][{3 Cos[-3 Pi/4/7] + 2,
     Cos[3 - 3 Pi/4], 5 + 2 Sin[-3 Pi/4 7]}]]
 ]