Sage's plot3d() does not accurately depict the domain

[sagetrac-drkirkby]

Following a request to test the following 3 lines of code on #8433

y=var('y')
B=plot3d(sqrt(sin(x)*sin(y)),(x,-2*pi,2*pi),(y,-2*pi,2*pi),viewer='tachyon')
B.show()

I did this on Sage 4.5.1 running on Solaris 10 and found no problems of excessive CPU time as reported at #8433. However, the quality of the output leaves a lot to be desired, and appears to show discontinuities which are not in the function.

Attached are two images showing the output from Sage using

y=var('y')
B=plot3d(sqrt(sin(x)*sin(y)),(x,-2*pi,2*pi),(y,-2*pi,2*pi),viewer='tachyon')
B.show()

and Mathematica 7.0.1 using the following command

Plot3D[Sqrt[Sin[x] Sin[y]],{x,-2 Pi, 2 Pi},{y, - 2 Pi, 2 Pi}] 

Whilst Mathematica's output is obviously more asetically pleasing, with the false colour, the main problem with the Sage output is that it shows discontinuities which simply should not exist in the function being plotted. (Obviously, for some values of x and y, the square root of a negative number is taken, so the plots do not show this. However, the transition to this point should be smooth, like in the Mathematica

It would be good if we could improve this. Jason Grout had some idea what the problem probably is.

http://groups.google.com/group/sage-devel/browse_thread/thread/7476ecc5d4e83caf?hl=en

saying

*I think the problem is that in Sage, we do not try to break up plotting triangles to find out the actual boundaries of a domain. Instead, we just try to plot the triangle that goes across the domain boundary, find that one corner of the triangle is off the domain, and so we don't plot the triangle. *

Related tickets #8433

CC: @jasongrout @robert-marik @robertwb @sagetrac-mhampton @sagetrac-mvngu

Component: graphics

Keywords: plot3d

Issue created by migration from https://trac.sagemath.org/ticket/10215

[sagetrac-drkirkby]

Attachment: sage-plot3d-sinx-siny.png

Plot produced by Sage 4.5.1 using plot3d(sqrt(sin(x)sin(y)),(x,-2pi,2pi),(y,-2pi,2*pi),viewer='tachyon')

[sagetrac-drkirkby]

Plot produced by Mathematica 7.0.1 using Plot3D[Sqrt[Sin[x] Sin[y]],{x,-2 Pi, 2 Pi},{y, - 2 Pi, 2 Pi}]

[sagetrac-drkirkby]

comment:2

Attachment: Plot3D-in-Mathematica-of-sqrt-sin-x-sin-y.png

[jasongrout]

comment:4

I made the topic of the ticket much more descriptive of the problem pointed out. If you'd like to open another ticket for another specific issue, feel free!

[sagetrac-drkirkby]

comment:5

Replying to @jasongrout:

I made the topic of the ticket much more descriptive of the problem pointed out. If you'd like to open another ticket for another specific issue, feel free!

That's fine by me.

[fchapoton]

Changed keywords from none to plot3d