RE: Filled Ellipsoid
- To: mathgroup at smc.vnet.net
- Subject: [mg27524] RE: [mg27505] Filled Ellipsoid
- From: "David Park" <djmp at earthlink.net>
- Date: Sat, 3 Mar 2001 03:40:04 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Boris,
Here is one method. We will need these packages:
Needs["Geometry`Rotations`"]
Needs["Graphics`Colors`"]
This is a parametric definition of an ellipse with a and b for axes lengths
and tilted at an angle theta. (You could also add translation terms to
center the ellipse at some other point.)
ellipse[theta_, a_, b_][t_] := RotationMatrix2D[-theta].{a Cos[t], b Sin[t]}
This converts the ellipse into a Line primitive. We plot, suppress the plot
display, and extract the primitive Line graphics which are the first part of
the Graphics output.
curve = First[ParametricPlot[Evaluate[
ellipse[Pi/4, 7, 3][t]], {t, 0, 2*Pi},
DisplayFunction -> Identity]];
This draws the ellipse as a filled area. We change Line to Polygon to obtain
a filled area colored Tomato. Then we change back to Black and draw the
curve to outline the area.
Show[Graphics[
{Tomato, curve /. Line -> Polygon,
Black, curve}], AspectRatio -> Automatic];
The DrawingPaperTutorial which goes with the DrawingPaper packages at my web
site has a section on drawing filled areas by various methods. DrawingPaper
makes it a little easier to extract the curve primitives from various plot
types and to manipulate the resulting data.
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
> From: Boris Breznen [mailto:bbreznen at vis.caltech.edu]
To: mathgroup at smc.vnet.net
>
> Is there a siple way to plot filled ellipsoid in Mathematica ? The basic
> Ellipsoid function, included in
> the Statistics`MultiDescriptiveStatistics` package plots a
> contour. I would
> like to
> fill it (simmilar to what Disc does with respect to Circle).
>
> Thank you,
>
> Boris Breznen
> bbreznen at vis.caltech.edu
>