#9664: Graphical representation of fans
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Reporter: vbraun | Owner: mhampton
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.6
Component: geometry | Keywords:
Author: Volker Braun | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by novoselt):
Hi Volker! So, here is my plan/proposal:
1. Make all "toric objects" plottable in a consistent way with options
trickling down from complicated objects to simpler ones.
1. Gather all these options in a single file, say
`sage.geometry.toric_plot` and use this module to store default options
with users being able to see all options, change them globally and reset
to originals. The same options also can be passed to each individual
object.
1. It is totally fine to have different internal functions for 2d and 3d
plots, but when possible options should have the same name/meaning.
1. I like your round 2-d fans, but I think there should be 3 ways to plot
fans (and other things): in the disk of given radius, in the box with
given sides (i.e. xyz-dimensions), and in the polytope determined by rays,
i.e. rays are drawn to primitive generators, and cones are drawn between
primitive generators. Reason - I think that round plots are pretty (so
people should use them and I propose this as default), boxed plots are
common (so people may want to use them despite of round ones being
prettier), and "generator plot" seems to be very natural from the point of
view of CPR-Fano toric varieties and I think this should be the default
for them.
1. I think that rays should be a little longer than cones, so that arrows
"stick out", and the length of these rays does not have to correlate with
primitive generators (but it would be nice to mark the generators with red
dots, or some other way to clearly distinguish them from other lattice
points).
1. What is the purpose of white strips surrounding rays in your
functions? (I agree that it looks pretty ;-))
Here are the options I think toric objects should have (each consequent
one accepts parameters for previous ones):
1. `ToricLatticeElement` (plots a point):
* `point_color`
* `point_size`
* `point_label`
* `point_label_shift` (so that it is not right on top of the point)
1. `ToricLattice` (plots all points within the given region):
* `plot_type` (one of "round", "box", "generators")
* `radius` (for "round", can also be given for "box" as all six bounds)
* `xyzmin/max` (six parameters)
1. `IntegralRayCollection`:
* `ray_color`
* `ray_thickness`
* `ray_extension` (how much longer should rays be compared to the size
based on other parameters, to make "arrows sticking out")
* `ray_label`
* `ray_label_shift`
* `generator_color` (for the lattice point corresponding to generator)
* `generator_size`
* `plot_lattice` (True/False to include lattice points or not)
1. `Cone`
* `cone_color`
* `cone_alpha`
* `cone_label`
* maybe something to determine label position, but it seems that it can
be position quite well between rays without necessity to shift it further
* `plot_rays` (True/False)
* `ray_label` can be given as a list of separate labels for each ray
(just indexing them may be not very good, e.g. for toric varieties it may
make sense to stick coordinate names next to rays)
1. `Fan`
* `plot_cones` (True/False)
* `cone_label` can be given as a list of separate labels for each cone
In 3-d cases there may be some sense in being able to specify options
differently for 2-d and 3-d cones, but that should be more clear in the
process. Also, instead of drawing points corresponding to generators,
maybe it is better to draw vectors, as in your implementation. But I still
would like to see rays continuing "to infinity", i.e. beyond shaded
regions for cones.
Thoughtscomments?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9664#comment:4>
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