On 5/27/10 10:35 PM, Vincent D wrote:
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.
I think that would be cool, even just from the standpoint of teaching
linear algebra or calc 3 and playing with linear transformations. And I
don't see why you'd need to limit it to things like Polygons. It would
be cool if you could do:
p=plot(whatever)
m*p # transform each coordinate
I think it would be very straightforward to do this using the underlying
2d matplotlib library, which has a very nice transformation framework
builtin [1] (in other words, we could probably easily just save up the
transformations, like we currently do with 3d plots, and then apply the
transformations on output, which should just be a matter of one or two
matplotlib calls at the very end right before drawing). On the 3d side,
Sage has a transformation framework, so it should be straightfoward to
make m*p do something cool there too.
I wonder if it would help if the graphics were inside the coercion system.
Jason
[1] http://matplotlib.sourceforge.net/devel/transformations.html
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