On 11/5/10 1:25 AM, Dr. David Kirkby wrote:
On 11/ 4/10 11:38 PM, David Joyner wrote:
sage:
plot3d(sqrt(sin(x)*sin(y)),(x,-2*pi,2*pi),(y,-2*pi,2*pi),plot_points=750)
and
sage:
B=plot3d(sqrt(sin(x)*sin(y)),(x,-2*pi,2*pi),(y,-2*pi,2*pi),plot_points=750,viewer='tachyon')
sage: B.show()
look better. I wonder what Mma uses as the default number of points.
Does anyone know if they are comparable with Sage's default?
As far as I know, Mathematica choses the point adaptively, so regions
where the function is changing rapidly get sampled more often. The
default is "Automatic" rather than fixed integer, though there is the
option "PlotPoints".
The documentation for Plot3D
http://reference.wolfram.com/mathematica/ref/Plot3D.html
says
"You should realize that with the finite number of sample points used,
it is possible for Plot3D to miss features in your functions. To check
your results, you should try increasing the settings for PlotPoints and
MaxRecursion."
Yep. But there's more than that. For example, try our example with
MaxRecursion->0. You'll see that it still gets the domain about right,
with a few artifacts in connecting the regions. It may just be that
they pick their triangles to start on the xy-plane. I suppose you could
test this by shifting the equation up by a small amount (say .05).
Thanks,
Jason
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