yet more surfaces in SAGE

[David Joyner]

Hi:
All these need:
sage: u = var("u")
sage: v = var("v")
Some interesting surfaces can be found here:
http://virtualmathmuseum.org/galleryS.html
- David Joyner

#Hyperhelicoidal
sage: fx = (sinh(v)*cos(3*u))/(1+cosh(u)*cosh(v))
sage: fy = (sinh(v)*sin(3*u))/(1+cosh(u)*cosh(v))
sage: fz = (cosh(v)*sinh(u))/(1+cosh(u)*cosh(v))
sage: parametric_plot3d([fx, fy, fz], (u, -pi, pi), (v, -pi, pi),
plot_points = [50,50], frame=False, color="red")

#Helicoid (lines through a helix)
#http://en.wikipedia.org/wiki/Helix
sage: fx = sinh(v)*sin(u)
sage: fy = -sinh(v)*cos(u)
sage: fz = 3*u
sage: parametric_plot3d([fx, fy, fz], (u, -pi, pi), (v, -pi, pi),
plot_points = [50,50], frame=False, color="red")

#Kuen's surface
#http://www.math.umd.edu/research/bianchi/Gifccsurfs/ccsurfs.html
sage: fx = (2*(cos(u) + u*sin(u))*sin(v))/(1+ u^2*sin(v)^2)
sage: fy = (2*(sin(u) - u*cos(u))*sin(v))/(1+ u^2*sin(v)^2)
sage: fz = log(tan(1/2 *v)) + (2*cos(v))/(1+ u^2*sin(v)^2)
sage: parametric_plot3d([fx, fy, fz], (u, 0, 2*pi), (v, 0.01,
pi-0.01), plot_points = [50,50], frame=False, color="green")

#5-pointed star
sage: fx = cos(u)*cos(v)*(abs(cos(1*u/4))^0.5 +
abs(sin(1*u/4))^0.5)^(-1/0.3)*(abs(cos(5*v/4))^1.7 +
abs(sin(5*v/4))^1.7)^(-1/0.1)
sage: fy = cos(u)*sin(v)*(abs(cos(1*u/4))^0.5 +
abs(sin(1*u/4))^0.5)^(-1/0.3)*(abs(cos(5*v/4))^1.7 +
abs(sin(5*v/4))^1.7)^(-1/0.1)
sage: fz = sin(u)*(abs(cos(1*u/4))^0.5 + abs(sin(1*u/4))^0.5)^(-1/0.3)
sage: parametric_plot3d([fx, fy, fz], (u, -pi/2, pi/2), (v, 0, 2*pi),
plot_points = [50,50], frame=False, color="green")

#a cool self-intersecting surface (Eppener surface?)
sage: fx = u - u^3/3 + u*v^2
sage: fy = v - v^3/3 + v*u^2
sage: fz = u^2 - v^2
sage: parametric_plot3d([fx, fy, fz], (u, -25, 25), (v, -25, 25),
plot_points = [50,50], frame=False, color="green")

#breather surface
#http://en.wikipedia.org/wiki/Breather_surface
sage: fx = (2*sqrt(0.84)*cosh(0.4*u)*(-(sqrt(0.84)*cos(v)*cos(sqrt(0.84)*v))
- sin(v)*sin(sqrt(0.84)*v)))/(0.4*((sqrt(0.84)*cosh(0.4*u))^2 +
(0.4*sin(sqrt(0.84)*v))^2))
sage: fy = (2*sqrt(0.84)*cosh(0.4*u)*(-(sqrt(0.84)*sin(v)*cos(sqrt(0.84)*v))
+ cos(v)*sin(sqrt(0.84)*v)))/(0.4*((sqrt(0.84)*cosh(0.4*u))^2 +
(0.4*sin(sqrt(0.84)*v))^2))
sage: fz = -u +
(2*0.84*cosh(0.4*u)*sinh(0.4*u))/(0.4*((sqrt(0.84)*cosh(0.4*u))^2 +
(0.4*sin(sqrt(0.84)*v))^2))
sage: parametric_plot3d([fx, fy, fz], (u, -13.2, 13.2), (v, -37.4,
37.4), plot_points = [90,90], frame=False, color="green")

[William Stein]

Please make a new trac ticket and post these there, OK?

--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org

[David Joyner]

Done. It's http://trac.sagemath.org/sage_trac/ticket/1857