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") --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-forum URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
