Hi David, Another really nice source of 3d plot examples in the OS X program "Grapher" that comes with every copy of OS X (in the Applications directory). It's quite nice.
-- William On Jan 18, 2008 9:41 AM, Jurgis Pralgauskis <[EMAIL PROTECTED]> wrote: > might try asking at http://k3dsurf.s4.bizhat.com/ > i attach k3dsurf source file, with these examples > > > On Jan 18, 2008 6:47 PM, David Joyner <[EMAIL PROTECTED]> wrote: > > > > On Jan 18, 2008 11:03 AM, Jurgis Pralgauskis > > <[EMAIL PROTECTED]> wrote: > > > > > > there are about 50 (if not more) surface examples in > > > http://k3dsurf.sourceforge.net/ > > > > > > Where? I can't find the docs and I'm having a hard time installing the > > program.... > > > > > > > > > > > > I mean, sage examples can borrow formulas :) > > > > > > > > > On Jan 18, 2008 5:29 PM, Hector Villafuerte <[EMAIL PROTECTED]> wrote: > > > > > > > > Nice plots, thanks David! > > > > About the cardiod, I gave it a try and started with this: > > > > > > > > var('t') > > > > a = 1 > > > > fx = a*cos(t)*(1-cos(t)) > > > > fy = a*sin(t)*(1-cos(t))*exp(-0.5*t) > > > > f1 = (fx, fy) > > > > parametric_plot(f1, 0, pi) > > > > > > > > which then extended to this: > > > > > > > > var('t v') > > > > a = 1 > > > > fx = a*cos(t)*(1-cos(t)) > > > > fy = a*sin(t)*(1-cos(t))*exp(-0.5*t)*cos(v) > > > > fz = a*sin(t)*(1-cos(t))*exp(-0.5*t)*sin(v) > > > > f = (fx, fy, fz) > > > > parametric_plot3d(f, (t,0,pi), (v,0,2*pi), rgbcolor='red') > > > > > > > > Will your wife settle for an apple instead? :) > > > > -- > > > > Hector > > > > > > > > > > > > > > > > On Jan 18, 2008 9:06 AM, William Stein <[EMAIL PROTECTED]> wrote: > > > > > On Jan 18, 2008 6:24 AM, David Joyner <[EMAIL PROTECTED]> wrote: > > > > > > > > > > > > Hi: > > > > > > > > > > > > Here are a few examples which I think are interesting. > > > > > > > > > > > > If anyone can figure out a way to plot a cardioid, > > > > > > http://mathworld.wolfram.com/HeartSurface.html, > > > > > > in SAGE, I'd be very interested. > > > > > > > > > > > > - David Joyner > > > > > > > > > > > > #M\"obius strip: > > > > > > sage: u,v = var("u,v") > > > > > > sage: p = parametric_plot3d([cos(u)*(1+v*cos(u/2)), > > > > > > sin(u)*(1+v*cos(u/2)), 0.2*v*sin(u/2)], (u,0, 4*pi), (v,0, > > > > > > 0.3),plot_points=[50,50]) > > > > > > > > > > > > #twisted ribbon > > > > > > sage: p = parametric_plot3d([3*sin(u)*cos(v), 3*sin(u)*sin(v), > > > > > > cos(v)], (u,0, 2*pi), (v, 0, pi),plot_points=[50,50]) > > > > > > > > > > > > #ellipsoid (automatically rescaled axes make it look spherical) > > > > > > sage: p = parametric_plot3d([3*sin(u)*cos(v), 2*sin(u)*sin(v), > > > > > > cos(u)], (u,0, 2*pi), (v, 0, 2*pi),plot_points=[50,50]) > > > > > > > > > > Use the aspect_ratio option: > > > > > > > > > > sage: var('u,v') > > > > > sage: parametric_plot3d([3*sin(u)*cos(v), 2*sin(u)*sin(v), cos(u)], > > > > > (u,0, 2*pi), (v, 0, 2*pi),plot_points=[50,50], aspect_ratio=[1,1,1]) > > > > > > > > > > I've attached a Sage worksheet that has all the plots in this email > > > > > rendered, > > > > > but with a few tweeks to make some of them work right or actually > > > > > work. > > > > > > > > > > Thanks! > > > > > > > > > > I'll be adding this to the examples section of parametric_plot3d. > > > > > > > > > > -- William > > > > > > > > > > > > > > > > > #cone > > > > > > sage: p = parametric_plot3d([u*cos(v), u*sin(v), u], (u, -1, 1), (v, > > > > > > 0, 2*pi), plot_points=[50,50]) > > > > > > > > > > > > #paraboloid > > > > > > sage: p = parametric_plot3d([u*cos(v), u*sin(v), u^2], (u, 0, 1), > > > > > > (v, > > > > > > 0, 2*pi), plot_points=[50,50]) > > > > > > > > > > > > #hyperboloid > > > > > > sage: p = plot3d(u^2-v^2, (u, -1, 1), (v, -1, 1), > > > > > > plot_points=[50,50]) > > > > > > > > > > > > #weird looking surface - like a M\"obius band but also an O > > > > > > sage: p = parametric_plot3d([sin(u)*cos(u)*log(u^2)*sin(v), > > > > > > (u^2)^(1/6)*(cos(u)^2)^(1/4)*cos(v), sin(v)], (u, -1, 1), (v, -pi, > > > > > > pi), plot_points=[50,50]) > > > > > > > > > > > > > > > > > > #a heart, but not a cardioid (for my wife) > > > > > > sage: p1 = parametric_plot3d([sin(u)*cos(u)*log(u^2)*v*(1-v)/2, > > > > > > ((u^6)^(1/20)*(cos(u)^2)^(1/4)-1/2)*v*(1-v), v^(0.5)], (u, 0.001, > > > > > > 1), > > > > > > (v, 0, 1), plot_points=[90,90]) > > > > > > sage: p2 = parametric_plot3d([-sin(u)*cos(u)*log(u^2)*v*(1-v)/2, > > > > > > ((u^6)^(1/20)*(cos(u)^2)^(1/4)-1/2)*v*(1-v), v^(0.5)], (u, 0.001, > > > > > > 1), > > > > > > (v, 0, 1), plot_points=[90,90]) > > > > > > sage: show(p1+p2, frame=False) > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > -- > > > > > William Stein > > > > > Associate Professor of Mathematics > > > > > University of Washington > > > > > http://wstein.org > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > -- > > > Jurgis Pralgauskis > > > omni: 8-616 77613; teledema: 8-657 65656; > > > jabber: [EMAIL PROTECTED]; skype: dz0rdzas; > > > > > > Don't worry, be happy :) and make things better ;) > > > > > > > > > > > > > > > > > > > > > > > > > > -- > Jurgis Pralgauskis > omni: 8-616 77613; teledema: 8-657 65656; > jabber: [EMAIL PROTECTED]; skype: dz0rdzas; > > Don't worry, be happy :) and make things better ;) > > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
