Bugfix hyperbolic_arc and hyperbolic_polygon

[sagetrac-skraemer]

If you draw an hyperbolic arc between two points with almost the same real part, it may result in a wrong arc.

You can see it as follows:

g = hyperbolic_triangle(-1+I, 1.0000000000001+I, 1000*I+1, fill = true);
g.set_axes_range(-1.5,1.5,-.5,2.5)
g.show()

CC: @videlec

Component: graphics

Keywords: hyperbolic_arc, hyperbolic_polygon

Author: Stefan Kraemer

Branch/Commit: adec9d2

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/19217

[sagetrac-skraemer]

Changed keywords from none to hyperbolic_arc, hyperbolic_polygon

[sagetrac-skraemer]

Author: skraemer

[sagetrac-skraemer]

Branch: u/skraemer/bugfix_hyperbolic_arc_and_hyperbolic_polygon

[sagetrac-skraemer]

Commit: 855f507

[sagetrac-skraemer]

New commits:

855f507

Bugfix for hyperbolic_arc and hyperbolic_polygon

[videlec]

comment:5

Hello,

Why 10^-3? Moreover it can be very wrong if the imaginary part is very small. Just try

sage: hyperbolic_triangle(0, 0.0001, 0.0001*I)

The above example just works fine without your patch.

Vincent

[videlec]

Reviewer: Vincent Delecroix

[sagetrac-skraemer]

comment:6

Hello Vincent,

thanks for reviewing my first patch!

Would a smaller boundary for the comparison be more eligible? Let's say 10^-12? Of course, the analogue example of ours will still produce a wrong result:

g = hyperbolic_triangle(0, 10**(-12),10**(-12)*I);g

But scaled to a larger region of hyperbolic geometry, it is quite hard to see:

g.set_axes_range(0,10**(-10),0,10**(-10));g

Or do you know a better way to compare a value to zero in sage?

best regards,
Stefan

[videlec]

comment:7

Hello,

Putting a smaller value would not solve anything. The main problem is that this subtelty should depend on the window parameters (i.e. xmin, xmax, ymin, ymax). Hence decided at the time you generate the image.

I have no miracle to propose.

Vincent

[sagetrac-git]

Changed commit from 855f507 to adec9d2

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

b3b9821	Bugfix hyperbolic_arc and hyperbolic_polygon
adec9d2	Bugfix for hyperbolic_arc and hyperbolic_polygon

[sagetrac-skraemer]

comment:9

Hello,

I guess, something went wrong with git. I am sorry for this. Please let me know, if it does not work.

I had a new idea, how to handle this issue: Instead of checking, whether the points are above each other, one could check, how much the line connecting the points differ by the circle through the points. A simple test for this is to look at the quotient of the length of the connecting line and the radius of the circle. If this quotient is smaller than 0.1, we choose a line. The parameter .1 was chosen by experiment.

In this version the reported bug does not appear and your examples work also.

best regards,
Stefan

[videlec]

Changed author from skraemer to Stefan Kraemer

[videlec]

comment:10

Hello,

Some trac administrative things:

• Once you are done with some modification, you should switch the status to needs review (it was in needs work).
• the Authors field should be with plain names (not the login)
  This is fine for now.

Your solution is great! I set to positive review and it will be soonly merge in the development release.

Vincent

[vbraun]

Changed branch from u/skraemer/bugfix_hyperbolic_arc_and_hyperbolic_polygon to adec9d2