Attached is a plot comparing the new approach (above) vs. a 750-edge polygonal approximation for the ellipses (based directly on James Evans' example). Here's a description of what it does:
Ellipses are normally drawn using an approximation that uses
eight cubic bezier splines. The error of this approximation
is 1.89818e-6, according to this unverified source:
Lancaster, Don. Approximating a Circle or an Ellipse Using
Four Bezier Cubic Splines.
http://www.tinaja.com/glib/ellipse4.pdf
There is a use case where very large ellipses must be drawn
with very high accuracy, and it is too expensive to render the
entire ellipse with enough segments (either splines or line
segments). Therefore, in the case where either radius of the
ellipse is large enough that the error of the spline
approximation will be visible (greater than one pixel offset
from the ideal), a different technique is used.
In that case, only the visible parts of the ellipse are drawn,
with each visible arc using a fixed number of spline segments
(8). The algorithm proceeds as follows:
1. The points where the ellipse intersects the axes bounding
box are located. (This is done be performing an inverse
transformation on the axes bbox such that it is relative to
the unit circle -- this makes the intersection calculation
much easier than doing rotated ellipse intersection
directly).
This uses the "line intersecting a circle" algorithm from:
Vince, John. Geometry for Computer Graphics: Formulae,
Examples & Proofs. London: Springer-Verlag, 2005.
2. The angles of each of the intersection points are
calculated.
3. Proceeding counterclockwise starting in the positive
x-direction, each of the visible arc-segments between the
pairs of vertices are drawn using the bezier arc
approximation technique implemented in Path.arc().
Cheers,
Mike
Ted Drain wrote:
All of these sound like good ideas to me. Just for some history: the original reason we worked w/ John to get an Ellipse primitive in (vs a normal line plot of sampled points) were to:- improve ellipse plotting speeds (we plot a LOT of them at once) - improve post script output Ted At 08:53 AM 12/10/2007, Michael Droettboom wrote:John Hunter wrote:On Dec 10, 2007 10:25 AM, Ted Drain <[EMAIL PROTECTED]> wrote:I don't know if the current MPL architecture can support this but it would be nice if it worked that way. We have people making decisions based on what these plots show that affect spacecraft worth hundredsof millions of dollars so it's important that we're plottingthings accurately.We can support this, but I think we would do this with an arc class rather than an ellipse class, and write a special case class that is viewlim aware.I agree -- I think there are two uses cases for ellipse that are in conflict here. One is these large ellipses, the other is for things like scatter plots, where speed and file size is more important than accuracy. My mind was probably stuck on the latter as I've worked along the transforms branch.A simple example of a line that has analogous behavior is examples/clippedline.py, which clips the points outside the viewport and draws in a different style according to the resolution of the viewlim. The reason I think it would be preferable to use an arc here is because we won't have to worry about filling the thing when we only approximate a section of it. You could feed in a 360 degree elliptical arc and then zoom into a portion of it. With the 8 point ellipse as is, and the addition of an arc class that does 4 or 8 point approximation within the zoom limits, should that serve your requirements?As a possible starting point, the transforms branch already has arc-approximation-by-cubic-bezier-spline code. It determines the number of splines to use based on the radians included in the arc, which is clearly not what we want here. But it should be reasonably straightforward to make that some fixed number and draw the arc between the edges of the axes. Or, alternatively, (and maybe this is what John is suggesting), the arc could be approximated by line segments (with the number of segments something like the number of pixels across the axes). To my naive mind, that seems more verifiable -- or at least it puts the responsibility of getting this right all in one place. IMHO, these spline approximation tricks are all just with the aim of pushing curve rendering deeper into the backends for speed and file size improvements. But obviously there needs to be a way around it when it matters. Cheers, Mike -- Michael Droettboom Science Software Branch Operations and Engineering Division Space Telescope Science Institute Operated by AURA for NASA ------------------------------------------------------------------------- SF.Net email is sponsored by: Check out the new SourceForge.net Marketplace. It's the best place to buy or sell services for just about anything Open Source. http://sourceforge.net/services/buy/index.php _______________________________________________ Matplotlib-devel mailing list Matplotlib-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/matplotlib-develTed Drain Jet Propulsion Laboratory [EMAIL PROTECTED]-------------------------------------------------------------------------SF.Net email is sponsored by: Check out the new SourceForge.net Marketplace.It's the best place to buy or sell services for just about anything Open Source. http://sourceforge.net/services/buy/index.php _______________________________________________ Matplotlib-devel mailing list Matplotlib-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/matplotlib-devel
-- Michael Droettboom Science Software Branch Operations and Engineering Division Space Telescope Science Institute Operated by AURA for NASA
<<inline: ellipse.png>>
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