Once you have opened a Maxima session, load package draw and then set global variable draw_renderer to vtk:
load("draw") $
draw_renderer: 'vtk $
The surface of a shell is the result of the displacement of an ellipse along an helico-spiral curve. The mathematical model used here is explained in this paper.
h(a,b,s):= 1/sqrt((cos(s)/a)^2+(sin(s)/b)^2) $
x(d,A,beta,phi,omega,mu,alpha,a,b,theta,s):=
d*(A*sin(beta) * cos(theta) +
h(a,b,s) * ( cos(s+phi)*cos(theta+omega) -
sin(mu)*sin(s+phi)*sin(theta+omega) )) *
exp(theta*cot(alpha))$
y(A,beta,phi,omega,mu,alpha,a,b,theta,s):=
(-A*sin(beta)*sin(theta)-
h(a,b,s) * ( cos(s+phi)*sin(theta+omega) +
sin(mu)*sin(s+phi)*cos(theta+omega) )) *
exp(theta*cot(alpha))$
z(A,beta,phi,mu,alpha,a,b,theta,s):=
(-A*cos(beta) + h(a,b,s)*sin(s+phi)*cos(mu)) *
exp(theta*cot(alpha))$
degree: %pi/180$
shell(d,A,beta,phi,omega,mu,alpha,a,b,thetamin,thetamax,smin,smax) :=
[background_color = navy,
axis_3d = false,
color = white,
xu_grid = 250,
yv_grid = 50,
parametric_surface(
x(d,A,beta,phi,omega,mu,alpha,a,b,theta,s),
y(A,beta,phi,omega,mu,alpha,a,b,theta,s),
z(A,beta,phi,mu,alpha,a,b,theta,s),
theta, thetamin, thetamax,
s, smin , smax)] $
Glycimeris glycimeris (Linnaeus, 1767).
(alpha:37*degree,
beta:90*degree,
phi:0*degree,
mu:1*degree,
omega:1*degree,
A:2,
a:2,
b:2.1,
d:1,
thetamin:0*%pi,
thetamax:8*%pi,
smin:0,
smax:2*%pi,
draw3d(
shell(
d,A,beta,phi,omega,mu,alpha,a,b,thetamin,thetamax,smin,smax)))$
Origin: Galician coast.
Barnea candida (Linnaeus, 1758).
(alpha:39*degree,
beta:50*degree,
phi:0*degree,
mu:1*degree,
omega:1*degree,
A:9000,
a:6500,
b:17000,
d:1,
thetamin:0*%pi,
thetamax:8*%pi,
smin:0,
smax:2*%pi,
draw3d(
shell(
d,A,beta,phi,omega,mu,alpha,a,b,thetamin,thetamax,smin,smax)) )$
Origin: Galician coast.
Turritella communis (Risso, 1824).
(alpha:88.9*degree,
beta:4*degree,
phi:55*degree,
mu:1*degree,
omega:-2*degree,
A:22.2,
a:1.3,
b:1.5,
d:1,
thetamin:0*%pi,
thetamax:25*%pi,
smin:0,
smax:2*%pi,
draw3d(
shell(
d,A,beta,phi,omega,mu,alpha,a,b,thetamin,thetamax,smin,smax)) )$
Origin: Galician coast.
Nucella lapillus (Linnaeus, 1758).
(alpha:86*degree,
beta:11*degree,
phi:-22*degree,
mu:0*degree,
omega:24*degree,
A:95,
a:20,
b:35,
d:1,
thetamin:-8*%pi,
thetamax:4*%pi,
smin:0,
smax:2*%pi,
draw3d(
shell(
d,A,beta,phi,omega,mu,alpha,a,b,thetamin,thetamax,smin,smax)) )$
Origin: Galician coast.
Dentalium vulgare (Da Costa, 1778).
(alpha:17*degree,
beta:80*degree,
phi:-30*degree,
mu:1*degree,
omega:-60*degree,
A:5,
a:0.4,
b:0.4,
d:1,
thetamin:-4*%pi,
thetamax:4*%pi,
smin:0,
smax:2*%pi,
draw3d(
shell(
d,A,beta,phi,omega,mu,alpha,a,b,thetamin,thetamax,smin,smax)) )$
Origin: Galician coast.
Spirula spirula (Linnaeus, 1758).
(alpha:78*degree,
beta:90*degree,
phi:1*degree,
mu:1*degree,
omega:1*degree,
A:2.1,
a:0.7,
b:0.7,
d:1,
thetamin:0*%pi,
thetamax:4*%pi,
smin:0,
smax:2*%pi,
draw3d(
shell(
d,A,beta,phi,omega,mu,alpha,a,b,thetamin,thetamax,smin,smax)) )$
Origin: Galician coast.
Nautilus sp.
(alpha:80*degree,
beta:90*degree,
phi:0*degree,
mu:0*degree,
omega:0*degree,
A:2,
a:2,
b:1.5,
d:1,
thetamin:0*%pi,
thetamax:8*%pi,
smin:0,
smax:2*%pi,
draw3d(
shell(
d,A,beta,phi,omega,mu,alpha,a,b,thetamin,thetamax,smin,smax)) )$
Origin: Pacific Ocean.
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