Hello,
It seems that Sage doesn't yet have tools to render nice pictures of
hyperbolic geometry. I would like to be able to plot fundamental
domains and tessellations for some Fuchsian groups (in the three
standard conformal models: half-plane, disc and hyperboloid). Has
anybody started some work in this direction? Does anybody have
interesting pointers on tools or algorithmic references in that
domain?
More generally, the way sage.plot is built seems to be dedicated
mostly to function graphs. Is it possible to attach geometric objects
to an underlying space? meaning that if I have a Square attached to
the euclidean plane, I would like to be able to act on it with a
matrix like in the following
{{{
sage: p = Polygon([(0,0),(0,1),(1,1)])
sage: m = matrix([[1,1],[0,1]])
sage: m*p # the polygon made of the points (0,0), (1,1), (2,1)
}}}
e.g. to see a Polygon more as a subset of an homogeneous space with a
complete metric than a plot object.
There is a patch in sage-combinat that is needed to plot the arc of
circles (which is called arc-vd.patch) but which is also available
here:
http://iml.univ-mrs.fr/~delecroi/arc-vd.patch
The file that contains a draft of hyperbolic geometry:
http://iml.univ-mrs.fr/~delecroi/hyperbolic_half_plane.py
A sage worksheet that explains how the thing works:
http://iml.univ-mrs.fr/~delecroi/polygon_in_hyperbolic_plane.sws
Thank you,
Vincent
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