there are about 50 (if not more) surface examples in
http://k3dsurf.sourceforge.net/
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 ;)
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