Steinbach Screw

Steinbach Screw

The Steinbach Screw is a mathematical three-dimensional
surface with the following parametric equation:

x = u cos(v)
y = u sin(v)
z = v cos(u)

Where u and v are iterated in a nested loop over the range:

u = -4.0 to 4.0 by 0.1
v = 0.0 to 6.25 by 0.05

Code:

for u=-4:0.05:4;
for v=0:0.05:6.25
X(round(u*10+41), round(v*20+1))=u*cos(v);
Y(round(u*10+41), round(v*20+1))=u*sin(v);
Z(round(u*10+41), round(v*20+1))=v*cos(u);
T(round(u*10+41), round(v*20+1))=u+v;
S(round(u*10+41), round(v*20+1))=u;
R(round(u*10+41), round(v*20+1))=v;
W(round(u*10+41), round(v*20+1))=u*v;
Q(round(u*10+41), round(v*20+1))=(u+4)^v;
end
end
[dZdu,dZdv]=gradient(Z);
dZ=sqrt(dZdu.^2+dZdv.^2);
surf(X,Y,Z,dZ)
light
colormap hsv(8)
colormap prism
shading interp
lighting phong
material shiny