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plottools

 ellipse
 generate 2-D plot object for an ellipse

 Calling Sequence ellipse(c, a, b, filled=boolean, numpoints=n, options)

Parameters

 c - center of the ellipse a - horizontal radius of the ellipse b - vertical radius of the ellipse filled=boolean - (optional) whether to fill the inside of the ellipse, default=false numpoints=n - (optional) number of points to generate, default=200 super, super=m, super=[m1,m2] - (optional) create a superellipse or generalized superellipse options - (optional) equations of the form option=value. For a complete list, see plot/options.

Description

 • The ellipse command creates a two-dimensional plot data object, which when displayed is an ellipse centered at c with radial distances a and b, that is, ellipse([x0, y0], a, b) draws the ellipse

$\frac{{\left(x-\mathrm{x0}\right)}^{2}}{{a}^{2}}+\frac{{\left(y-\mathrm{y0}\right)}^{2}}{{b}^{2}}=1$

 • The super option given alone is equivalent to super=m (with m=4) which is equivalent to super=[m,m]. More generally ellipse([x0, y0], a, b, super=[m1,m2]) draws the superellipse (or generalized superellipse when $\mathrm{m1}\ne \mathrm{m2}$)

${\left|\frac{x-\mathrm{x0}}{a}\right|}^{\mathrm{m1}}+{\left|\frac{y-\mathrm{y0}}{b}\right|}^{\mathrm{m2}}=1$

 • The plot data object produced by the ellipse command can be used in a PLOT data structure, or displayed using the plots[display] command.
 • Remaining arguments are interpreted as options, which are specified as equations of the form option = value. For more information, see plottools and plot/options.

Examples

 > $\mathrm{with}\left(\mathrm{plottools}\right):$
 > $\mathrm{with}\left(\mathrm{plots}\right):$

Draw an ellipse described by the following equation,

 > $a≔2:$$b≔3:$$\mathrm{x0}≔0:$$\mathrm{y0}≔0:$
 > $\mathrm{elli}≔\mathrm{ellipse}\left(\left[\mathrm{x0},\mathrm{y0}\right],a,b,\mathrm{filled}=\mathrm{true},\mathrm{color}=\mathrm{blue}\right):$
 > $\mathrm{display}\left(\mathrm{elli},\mathrm{scaling}=\mathrm{constrained}\right)$ which is equivalent (apart from the filled option) to:

 > $\mathrm{eq}≔\frac{{\left(x-\mathrm{x0}\right)}^{2}}{{a}^{2}}+\frac{{\left(y-\mathrm{y0}\right)}^{2}}{{b}^{2}}=1:$
 > $\mathrm{implicitplot}\left(\mathrm{eq},x=-4..4,y=-4..4,\mathrm{scaling}=\mathrm{constrained}\right)$ Ellipse in arbitrary forms can be generated with object transformations such as rotate in the plots package.

 > $\mathrm{display}\left(\mathrm{rotate}\left(\mathrm{elli},\frac{\mathrm{\pi }}{4}\right)\right)$ > $\mathrm{display}\left(\mathrm{ellipse}\left(\mathrm{super}\right),\mathrm{scaling}=\mathrm{constrained}\right)$ > $\mathrm{ms}≔\left[\frac{1}{3},\frac{1}{2},\frac{2}{3},1,\frac{3}{2},2,3,5\right]$
 ${\mathrm{ms}}{≔}\left[\frac{{1}}{{3}}{,}\frac{{1}}{{2}}{,}\frac{{2}}{{3}}{,}{1}{,}\frac{{3}}{{2}}{,}{2}{,}{3}{,}{5}\right]$ (1)
 > $\mathrm{display}\left(\mathrm{seq}\left(\mathrm{ellipse}\left(\mathrm{super}=\mathrm{ms}\left[i\right],\mathrm{legend}=\mathrm{cat}\left("m=",\mathrm{ms}\left[i\right]\right),\mathrm{color}="Niagara"‖i\right),i=1..\mathrm{nops}\left(\mathrm{ms}\right)\right),\mathrm{scaling}=\mathrm{constrained}\right)$ > $\mathrm{display}\left(\mathrm{ellipse}\left(\mathrm{super}=\left[\frac{1}{5},3\right],\mathrm{color}="DarkRed"\right),\mathrm{ellipse}\left(\mathrm{super}=\left[2,5\right],\mathrm{color}="DarkBlue"\right),\mathrm{scaling}=\mathrm{constrained}\right)$ Compatibility

 • The plottools[ellipse] command was updated in Maple 2019.
 • The super option was introduced in Maple 2019.