#1888: [with code] 3d graphics -- cool plots of space curves (examples for
docstrings)
-------------------------+--------------------------------------------------
Reporter: was | Owner: was
Type: enhancement | Status: closed
Priority: major | Milestone: sage-duplicate/invalid/wontfix
Component: graphics | Resolution: invalid
Keywords: | Work_issues:
Author: | Reviewer:
Merged: |
-------------------------+--------------------------------------------------
Changes (by mhansen):
* status: needs_work => closed
* resolution: => invalid
* milestone: sage-4.2 => sage-duplicate/invalid/wontfix
Old description:
> These need to be nicely test, sped up, etc., then
> made into docstrings:
>
> {{{
> Here are a few cool space curves.
> I'd like to make more from
> http://www.math.umd.edu/research/bianchi/Gifspacecurves/spcu.html
> and
> http://virtualmathmuseum.org/SpaceCurves/
> If anyone knows of some parametric equations for them, I'd appreciate it.
>
> #trefoil knot
> #http://en.wikipedia.org/wiki/Trefoil_knot
> sage: fx = 0.01*(41*cos(t) - 18*sin(t) - 83*cos(2*t)-83*sin(2*t) -
> 11*cos(3*t) + 27*sin(3*t))
> sage: fy = 0.01*(36*cos(t) + 27*sin(t) - 113*cos(2*t)+30*sin(2*t) +
> 11*cos(3*t) - 27*sin(3*t))
> sage: fz = 0.01*(45*sin(t) - 30*cos(2*t) + 113*sin(2*t)-11*cos(3*t) +
> 27*sin(3*t))
> sage: parametric_plot3d( (fx, fy, fz), (t, 0, 6*pi), plot_points =
> 500, frame=False)
>
> #figure-eight knot
> #http://en.wikipedia.org/wiki/Figure-eight_knot_%28mathematics%29
> sage: fx = (2 + cos(2*t))*cos(3*t)
> sage: fy = (2 + cos(2*t))*sin(3*t)
> sage: fz = sin(4*t)
> sage: parametric_plot3d( (fx, fy, fz), (t, 0, 6*pi), plot_points =
> 500, frame=False)
>
> #Cinquefoil Knot (a=2 is this one):
> #http://en.wikipedia.org/wiki/Skein_relation
> #http://virtualmathmuseum.org/SpaceCurves/index.html#Classic
> fx = cos(t)*(2 - cos(2a*t/(2*a + 1)))
> fy = sin(t)*(2 - cos(2*t/(2*a + 1)))
> fz = - sin(2*t/(2*a + 1))
> sage: parametric_plot3d( (fx, fy, fz), (t, 0, 20*pi), plot_points =
> 500, frame=False)
>
> #3-leafed space curve
> sage: a = 1; b = 1; c = 1; d = 3; e = 2
> sage: fx = (a + b*cos(d*t))*cos(e*t)
> sage: fy = (a + b*cos(d*t))*sin(e*t)
> sage: fz = c*sin(d*t)
> sage: parametric_plot3d( (fx, fy, fz), (t, 0, 4*pi), plot_points =
> 100, frame=False)
>
> # The Viviani Curve
> #http://en.wikipedia.org/wiki/Viviani's_curve
> sage: a = 1
> sage: fx = a*2*sin(t/2)
> sage: fy = a*sin(t)
> sage: fz = a*(1 + cos(t))
> sage: parametric_plot3d( (fx, fy, fz), (t, 0, 4*pi), plot_points =
> 100, frame=False)
>
> #loxodrome
> #http://en.wikipedia.org/wiki/Loxodrome
> sage: fx = sin(t)/sqrt(1+t^2)
> sage: fy = cos(t)/sqrt(1+t^2)
> sage: fz = t/sqrt(1+t^2)
> sage: parametric_plot3d( (fx, fy, fz), (t, -4*pi, 4*pi), plot_points =
> 100, frame=False)
> }}}
New description:
These need to be nicely test, sped up, etc., then
made into docstrings:
{{{
Here are a few cool space curves.
I'd like to make more from
http://www.math.umd.edu/research/bianchi/Gifspacecurves/spcu.html
and
http://virtualmathmuseum.org/SpaceCurves/
If anyone knows of some parametric equations for them, I'd appreciate it.
#trefoil knot
#http://en.wikipedia.org/wiki/Trefoil_knot
sage: fx = 0.01*(41*cos(t) - 18*sin(t) - 83*cos(2*t)-83*sin(2*t) -
11*cos(3*t) + 27*sin(3*t))
sage: fy = 0.01*(36*cos(t) + 27*sin(t) - 113*cos(2*t)+30*sin(2*t) +
11*cos(3*t) - 27*sin(3*t))
sage: fz = 0.01*(45*sin(t) - 30*cos(2*t) + 113*sin(2*t)-11*cos(3*t) +
27*sin(3*t))
sage: parametric_plot3d( (fx, fy, fz), (t, 0, 6*pi), plot_points =
500, frame=False)
#figure-eight knot
#http://en.wikipedia.org/wiki/Figure-eight_knot_%28mathematics%29
sage: fx = (2 + cos(2*t))*cos(3*t)
sage: fy = (2 + cos(2*t))*sin(3*t)
sage: fz = sin(4*t)
sage: parametric_plot3d( (fx, fy, fz), (t, 0, 6*pi), plot_points =
500, frame=False)
#Cinquefoil Knot (a=2 is this one):
#http://en.wikipedia.org/wiki/Skein_relation
#http://virtualmathmuseum.org/SpaceCurves/index.html#Classic
fx = cos(t)*(2 - cos(2a*t/(2*a + 1)))
fy = sin(t)*(2 - cos(2*t/(2*a + 1)))
fz = - sin(2*t/(2*a + 1))
sage: parametric_plot3d( (fx, fy, fz), (t, 0, 20*pi), plot_points =
500, frame=False)
#3-leafed space curve
sage: a = 1; b = 1; c = 1; d = 3; e = 2
sage: fx = (a + b*cos(d*t))*cos(e*t)
sage: fy = (a + b*cos(d*t))*sin(e*t)
sage: fz = c*sin(d*t)
sage: parametric_plot3d( (fx, fy, fz), (t, 0, 4*pi), plot_points =
100, frame=False)
# The Viviani Curve
#http://en.wikipedia.org/wiki/Viviani's_curve
sage: a = 1
sage: fx = a*2*sin(t/2)
sage: fy = a*sin(t)
sage: fz = a*(1 + cos(t))
sage: parametric_plot3d( (fx, fy, fz), (t, 0, 4*pi), plot_points =
100, frame=False)
#loxodrome
#http://en.wikipedia.org/wiki/Loxodrome
sage: fx = sin(t)/sqrt(1+t^2)
sage: fy = cos(t)/sqrt(1+t^2)
sage: fz = t/sqrt(1+t^2)
sage: parametric_plot3d( (fx, fy, fz), (t, -4*pi, 4*pi), plot_points =
100, frame=False)
}}}
--
Comment:
There are already a ton of examples (almost annoyingly many) in the
docstring for parametric_plot3d. I don't think that adding the few listed
here is helpful at this point.
If someone really wants to add them, then they can repoen this ticket.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/1888#comment:7>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
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-trac?hl=en
-~----------~----~----~----~------~----~------~--~---
