#5514: [with patch, needs work] implement exclusions for parametric 3d plots
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Reporter: wcauchois | Owner: wcauchois
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.0.1
Component: graphics | Keywords:
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Comment(by jason):
Replying to [comment:13 wcauchois]:
>
> IndexFaceSet computes the bounding box by finding the min/max of its
vertices. The problem you describe appears to occur because we don't
remove all of the unused vertices. The issue is somewhat subtle since if
we remove a face, that does not necessarily mean the vertices that it
references are not in use by another face. One way to solve this problem
would be to maintain an array of reference counts for every vertex while
we are clipping the region. At the end of the method, we could delete
vertices with a reference count of 0. This seems like overkill though --
perhaps we can use assumptions about the structure of the parametric
surface (a rectangular grid).
I believe the {{{_clean_point_list}}} function clears out unused points
(implementing the functionality that Bill describes above). However, we
don't call this (i.e., we commented out the existing call to this) so that
we can still get an easy correspondence between the parameter values and
the points generated (i.e., the points are still in a grid of parameter
values, as long as none are missing).
* We could bolt one more thing on---a bitset of the points that are
used. We could use the bitset class in misc/bitset.pxi for that.
* Or we could just store the parameter values with each point. This
would also make us more flexible in handling the situation below.
We need this correspondence between vertices and parameter values so that
we can clip based on the parameter values.
>
> > 2. I thought maybe something like[[BR]]
> > {{{plot3d(sqrt(6-2*x^2-5*y^2), (x, -sqrt(3), sqrt(3)), (y, -1, 1),
region_function=lambda x,y: 6-2*x^2-6*y^2>0)}}}[[BR]]
> > would now be possible, but it appears the clip comes after the
evaluations, thus this raises an error for the negatives in the square
root. So maybe this should be handled with some sort of piecewise
definition for the function and then the excess would be clipped by a
{{{region_function}}} before showing it.
> >
> > OK, thinking while I write - here's a hack - insert an absolute value,
then trim:[[BR]]
> > {{{plot3d(sqrt(abs(6-2*x^2-5*y^2)), (x, -sqrt(3), sqrt(3)), (y, -1,
1), region_function=lambda x,y: 6-2*x^2-6*y^2>0)}}}
>
> That's because the clipping is done after the function is evaluated at
every (u,v) coordinate. Maybe we should modify eval_grid so that it does
not perform this unecessary (and sometimes troublesome) computation.
So, we could:
* make it so that the region passed into the plot3d command is used
during the initial evaluation; if the point passes the region function,
then a vertex is calculated from it. This would probably save time
anyway. If we do this, we need to take into account the different
signatures of region functions. For a two-argument function, check before
the vertex is calculated, and for a three- or five-argument region
function, check after the vertex is calculated (because the arguments to
the region function include the vertex coordinates). Because of this last
possibility, we probably also want to also
* make the indexed face sets handle evaluations which throw errors, in a
similar way that 2d plotting handles undefined values. This would also
probably necessitate storing the parameter values with the vertices.
Either way, we violate the assumption that the vertices are from a grid of
parameter values. We probably will have to store the parameter values
that generate each vertex.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5514#comment:14>
Sage <http://sagemath.org/>
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