#10132: Parametrization of (metric) surfaces in 3D euclidean space
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Reporter: mikarm | Owner:
mikarm
Type: enhancement | Status:
needs_work
Priority: major | Milestone:
sage-5.0
Component: geometry | Resolution:
Keywords: differential geometry, parametrized surface | Work issues:
Report Upstream: N/A | Reviewers:
vdelecroix
Authors: Mikhail Malakhaltsev, Joris Vankerschaver | Merged in:
Dependencies: #11549 | Stopgaps:
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Changes (by vdelecroix):
* status: needs_review => needs_work
Comment:
Hello,
Sorry for the (very) long delay between the first and the second review.
1) I was not able to build the documentation. Launching "sage -docbuild
reference html" gives me an error saying that riemannian_manifols is not
found (on sage-5.0.beta7). More precisely, I get "WARNING: toctree
contains reference to nonexisting document
u'sage/geometry/riemannian_manifolds/parametrized_surface3d"
Then the file for parametrized surfaces is not available in the reference
manual. Does it work for you ?
2) In order to make it more user friendly I suggest to add some predefined
surfaces that may be accessible like in the following example
{{{
sage: surfaces.Sphere(center=(0,0,0), radius=2))
...
}}}
A non exhaustive list of constructor would be: sphere, torus, cylinder,
ellipsoid, revolution (for surface of revolution). This will simplify the
whole documentation as the examples may be built from those constructor.
You may take a look at graphs which allow such feature
{{{
sage: graphs.CycleGraph(4)
Cycle graph: Graph on 4 vertices
}}}
Depending on your feeling, it's possible to put this in another ticket
(that I can do).
3) You do use a lot of cached_method that are sometimes redundant. As an
example first_fundamental_form_coefficients and
_compute_first_fundamental_form_coefficient are two cached function. But
the first one only calls the latter for different values. This remark also
applies to second_fundamental_form_coefficients.
4) The most interesting part of your patch is the numerical integration
for geodesic and parallel transport. But, you did not put any funny
example! It would be interesting to have a plotted example of geodesic (on
the sphere, ...) and parallel transport (along a loop on a cone, along two
paths joinging the same points on the sphere, ...)
Anyway, the patch is very nice.
More to come,
Vincent
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10132#comment:61>
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