Hello! How can I plot Viviani's curve in Sage onto cylinder and sphere? My problem is putting sphere into or inside cylinder and then put Viviani's Curve on this.
here is example http://upload.wikimedia.org/wikipedia/commons/0/05/Viviani_curve.png
Here is a full working example that semi-resembles the original example on Wikipedia:
var('u v')
sph_obj = parametric_plot3d(
(sin(u)*cos(v), sin(u)*sin(v), cos(u)),
(v, 0, 2*pi),
(u, 0, 2*pi),
opacity=0.3,
color=(0.2, 0.1, 0.1),
)
cyl_obj = parametric_plot3d(
(sin(v)/2, cos(v)/2 + 1/2, u),
(v, 0, 2*pi),
(u, -3/2, 3/2),
opacity=0.7,
color=(0.2, 0.2, 0.3),
plot_points=(80, 3)
)
v_curve_obj = parametric_plot3d(
(sin(v)*cos(v), sin(v)*sin(v), cos(v)),
(v, 0, 2*pi),
color="green",
thickness=2,
)
(sph_obj + cyl_obj + v_curve_obj).rotateZ(3/2).show(
viewer="tachyon",
aspect_ratio=1,
frame=False,
zoom=1.3
)
Thank you for quick answer! But still we have a problem with plotting. We have this equasions: for sphere:
parametric_plot3d((sin(u)*cos(v),sin(u)*sin(v),cos(u)),(v,0,2*pi),(u,0,2*pi))
for cylinder:
parametric_plot3d((sin(v),cos(v),u),(v,0,2*pi),(u,0,2*pi))
and viviani's curve:
parametric_plot3d((sin(v)*cos(v),sin(v)*sin(v),cos(v)),(v,0,2*pi))
and now we don't know how to put it all together. :(
If you have a parametrization of the curve, then parametric_plot3d will probably be the best way to plot the curve. Spheres and cylinders are easy to plot -- here is one example:
S = sphere((0,1,2),2,opacity=.6)
theta,z=var('theta,z')
C = cylindrical_plot3d(2,(theta,0,4*pi/2),(z,-2,2),opacity=.5,color='red')
(S+C).show(aspect_ratio=1)
Asked: 2011-05-19 12:18:07 +0200
Seen: 1,053 times
Last updated: May 19 '11
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