⚠️ Warning: This is a draft ⚠️

This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.

If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.

A [[wp:superellipse|superellipse]] is a geometric figure defined as the set of all points (x, y) with

::: $\left|\frac\left\{x\right\}\left\{a\right\}\right|^n! + \left|\frac\left\{y\right\}\left\{b\right\}\right|^n! = 1,$

where ''n'', ''a'', and ''b'' are positive numbers.

;Task Draw a superellipse with n = 2.5, and a = b = 200

## C

Interactive program to draw a SuperEllipse. Requires the [http://www.cs.colorado.edu/~main/bgi/cs1300/ WinBGIm] library.


#include<graphics.h>
#include<stdio.h>
#include<math.h>

#define pi M_PI

int main(){

double a,b,n,i,incr = 0.0001;

printf("Enter major and minor axes of the SuperEllipse : ");
scanf("%lf%lf",&a,&b);

printf("Enter n : ");
scanf("%lf",&n);

initwindow(500,500,"Superellipse");

for(i=0;i<2*pi;i+=incr){
putpixel(250 + a*pow(fabs(cos(i)),2/n)*(pi/2<i && i<3*pi/2?-1:1),250 + b*pow(fabs(sin(i)),2/n)*(pi<i && i<2*pi?-1:1),15);
}

printf("Done. %lf",i);

getch();

closegraph();
}


## EchoLisp

Link to the super-ellipse [http://www.echolalie.org/echolisp/images/super-ellipse.png image].


(lib 'plot)
(define (eaxpt x n) (expt (abs x) n))
(define (Ellie x y) (+ (eaxpt (// x 200) 2.5) (eaxpt (// y 200) 2.5) -1))

(plot-xy Ellie -400 -400)
→ (("x:auto" -400 400) ("y:auto" -400 400))



## FreeBASIC

' version 23-10-2016
' compile with: fbc -s console

Const scr_x = 800       ' screen 800 x 800
Const scr_y = 600
Const m_x = scr_x \ 2   ' middle of screen
Const m_y = scr_y \ 2

Sub superellipse(a As Long, b As Long, n As Double)

ReDim As Long y(0 To a)
Dim As Long x

y(0) = b ' value for x = 0
y(a) = 0 ' value for x = a

'(0,0) is in upper left corner

PSet (m_x, m_y - y(0)) ' set starting point

For x = 1 To a-1
y(x) = Int( Exp( Log(1 - ((x / a) ^ n)) / n ) * b )
Line - ((m_x + x), (m_y - y(x)))
Next

For x = a To 0 Step -1
Line - ((m_x + x), (m_y + y(x)))
Next

For x = 0 To a
Line - ((m_x - x), (m_y + y(x)))
Next

For x = a To 0 Step -1
Line - ((m_x - x), (m_y - y(x)))
Next

End Sub

' ------=< MAIN >=------

ScreenRes scr_x, scr_y, 32

Dim As Long   a = 200
Dim As Long   b = 150
Dim As Double n = 2.5

superellipse(a, b, n)

' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End


## Go

package main

import (
"github.com/fogleman/gg"
"math"
)

/* assumes a and b are always equal */
func superEllipse(dc *gg.Context, n float64, a int) {
hw := float64(dc.Width() / 2)
hh := float64(dc.Height() / 2)

// calculate y for each x
y := make([]float64, a+1)
for x := 0; x <= a; x++ {
aa := math.Pow(float64(a), n)
xx := math.Pow(float64(x), n)
y[x] = math.Pow(aa-xx, 1.0/n)
}

for x := a; x >= 0; x-- {
dc.LineTo(hw+float64(x), hh-y[x])
}
for x := 0; x <= a; x++ {
dc.LineTo(hw+float64(x), hh+y[x])
}
for x := a; x >= 0; x-- {
dc.LineTo(hw-float64(x), hh+y[x])
}
for x := 0; x <= a; x++ {
dc.LineTo(hw-float64(x), hh-y[x])
}

dc.SetRGB(1, 1, 1) // white ellipse
dc.Fill()
}

func main() {
dc := gg.NewContext(500, 500)
dc.SetRGB(0, 0, 0) // black background
dc.Clear()
superEllipse(dc, 2.5, 200)
dc.SavePNG("superellipse.png")
}


{{out}}


Image similar to J entry.



Use the [https://github.com/ghcjs/ghcjs ghcjs compiler ] to compile to JavaScript that runs in a browser. The [https://github.com/reflex-frp/reflex-dom reflex-dom ] library is used to help with SVG rendering and input.

{-# LANGUAGE OverloadedStrings, RankNTypes #-}
import Reflex
import Reflex.Dom
import Data.Text (Text, pack, unpack)
import Data.Map (Map, fromList, empty)

width = 600
height = 500

type Point = (Float,Float)
type Segment = (Point,Point)

data Ellipse = Ellipse {a :: Float, b :: Float, n :: Float}

toFloat :: Text -> Maybe Float

toEllipse :: Maybe Float -> Maybe Float -> Maybe Float -> Maybe Ellipse
toEllipse (Just a) (Just b) (Just n) =
if a < 1.0 || b <= 1.0 || n <= 0.0  -- not all floats are valid
then Nothing
else Just $Ellipse a b n toEllipse _ _ _ = Nothing showError :: Maybe a -> String showError Nothing = "invalid input" showError _ = "" reflect45 pts = pts ++ fmap (\(x,y) -> ( y, x)) (reverse pts) rotate90 pts = pts ++ fmap (\(x,y) -> ( y, -x)) pts rotate180 pts = pts ++ fmap (\(x,y) -> (-x, -y)) pts scale a b = fmap (\(x,y) -> ( a*x, b*y )) segments pts = zip pts$ tail pts

toLineMap :: Maybe Ellipse -> Map Int ((Float,Float),(Float,Float))
toLineMap (Just (Ellipse a b n)) =
let f p = (1 - p**n)**(1/n)
dp = iterate (*0.9) 1.0
ip = map (\p -> 1.0 -p) dp
points s =
if n > 1.0
then (\p -> zip p (map f p)) ip
else (\p -> zip (map f p) p) dp

in fromList $-- changes list to map (for listWithKey) zip [0..]$ -- annotates segments with index
segments $-- changes points to line segments scale a b$
rotate180 $-- doubles the point count rotate90$  -- doubles the point count
reflect45 $-- doubles the point count takeWhile (\(x,y) -> x < y )$ -- stop at 45 degree line
points 0.9

toLineMap Nothing = empty

lineAttrs :: Segment -> Map Text Text
lineAttrs ((x1,y1), (x2,y2)) =
fromList [ ( "x1",    pack $show (width/2+x1)) , ( "y1", pack$ show (height/2+y1))
, ( "x2",    pack $show (width/2+x2)) , ( "y2", pack$ show (height/2+y2))
, ( "style", "stroke:brown;stroke-width:2")
]

showLine :: MonadWidget t m => Int -> Dynamic t Segment -> m ()
showLine _ dSegment = do
elSvgns "line" (lineAttrs <$> dSegment)$ return ()
return ()

main = mainWidget $do elAttr "h1" ("style" =: "color:brown")$ text "Superellipse"
ta <- el "div" $do text "a: " textInput def { _textInputConfig_initialValue = "200"} tb <- el "div"$ do
text "b: "
textInput def { _textInputConfig_initialValue = "200"}

tn <- el "div" $do text "n: " textInput def { _textInputConfig_initialValue = "2.5"} let ab = zipDynWith toEllipse (toFloat <$> value ta) (toFloat <$> value tb) dEllipse = zipDynWith ($) ab (toFloat <$> value tn) dLines = fmap toLineMap dEllipse dAttrs = constDyn$ fromList
[ ("width" , pack $show width) , ("height", pack$ show height)
]
elAttr "div" ("style" =: "color:red") $dynText$ fmap (pack.showError) dEllipse
el "div" $elSvgns "svg" dAttrs$ listWithKey dLines showLine
return ()

-- At end to avoid Rosetta Code unmatched quotes problem.
elSvgns :: forall t m a. MonadWidget t m => Text -> Dynamic t (Map Text Text) -> m a -> m (El t, a)
elSvgns = elDynAttrNS' (Just "http://www.w3.org/2000/svg")


## J

[[File:J-superellipse.png|200px|thumb|right]]

We will fill the ellipse so that we do not have to worry about the size and shape of our pixels:

selips=: 4 :0
'n a b'=. y
1 >: ((n^~a%~]) +&|/ n^~b%~]) i:x
)

require'viewmat'
viewmat 300 selips 2.5 200 200


## Java

[[File:superellipse.png|300px|thumb|right]] {{works with|Java|8}}

import java.awt.*;
import java.awt.geom.Path2D;
import static java.lang.Math.pow;
import java.util.Hashtable;
import javax.swing.*;
import javax.swing.event.*;

public class SuperEllipse extends JPanel implements ChangeListener {
private double exp = 2.5;

public SuperEllipse() {
setPreferredSize(new Dimension(650, 650));
setBackground(Color.white);
setFont(new Font("Serif", Font.PLAIN, 18));
}

void drawGrid(Graphics2D g) {
g.setStroke(new BasicStroke(2));
g.setColor(new Color(0xEEEEEE));

int w = getWidth();
int h = getHeight();
int spacing = 25;

for (int i = 0; i < w / spacing; i++) {
g.drawLine(0, i * spacing, w, i * spacing);
g.drawLine(i * spacing, 0, i * spacing, w);
}
g.drawLine(0, h - 1, w, h - 1);

g.setColor(new Color(0xAAAAAA));
g.drawLine(0, w / 2, w, w / 2);
g.drawLine(w / 2, 0, w / 2, w);
}

void drawLegend(Graphics2D g) {
g.setColor(Color.black);
g.setFont(getFont());
g.drawString("n = " + String.valueOf(exp), getWidth() - 150, 45);
g.drawString("a = b = 200", getWidth() - 150, 75);
}

void drawEllipse(Graphics2D g) {

final int a = 200; // a = b
double[] points = new double[a + 1];

Path2D p = new Path2D.Double();
p.moveTo(a, 0);

for (int x = a; x >= 0; x--) {
points[x] = pow(pow(a, exp) - pow(x, exp), 1 / exp); // solve for y
p.lineTo(x, -points[x]);
}

// mirror to others
for (int x = 0; x <= a; x++)
p.lineTo(x, points[x]);

for (int x = a; x >= 0; x--)
p.lineTo(-x, points[x]);

for (int x = 0; x <= a; x++)
p.lineTo(-x, -points[x]);

g.translate(getWidth() / 2, getHeight() / 2);
g.setStroke(new BasicStroke(2));

g.setColor(new Color(0x25B0C4DE, true));
g.fill(p);

g.setColor(new Color(0xB0C4DE)); // LightSteelBlue
g.draw(p);
}

@Override
public void paintComponent(Graphics gg) {
super.paintComponent(gg);
Graphics2D g = (Graphics2D) gg;
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
g.setRenderingHint(RenderingHints.KEY_TEXT_ANTIALIASING,
RenderingHints.VALUE_TEXT_ANTIALIAS_ON);

drawGrid(g);
drawLegend(g);
drawEllipse(g);
}

@Override
public void stateChanged(ChangeEvent e) {
JSlider source = (JSlider) e.getSource();
exp = source.getValue() / 2.0;
repaint();
}

public static void main(String[] args) {
SwingUtilities.invokeLater(() -> {
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setTitle("Super Ellipse");
f.setResizable(false);
SuperEllipse panel = new SuperEllipse();

JSlider exponent = new JSlider(JSlider.HORIZONTAL, 1, 9, 5);
exponent.setMajorTickSpacing(1);
exponent.setPaintLabels(true);
exponent.setBackground(Color.white);
exponent.setBorder(BorderFactory.createEmptyBorder(20, 20, 20, 20));

Hashtable<Integer, JLabel> labelTable = new Hashtable<>();
for (int i = 1; i < 10; i++)
labelTable.put(i, new JLabel(String.valueOf(i * 0.5)));
exponent.setLabelTable(labelTable);

f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
});
}
}


## JavaScript


var n = 2.5, a = 200, b = 200, ctx;

function point( x, y ) {
ctx.fillRect( x, y, 1, 1);
}

function start() {
var can = document.createElement('canvas');
can.width  = can.height = 600;
ctx = can.getContext( "2d" );
ctx.rect( 0, 0, can.width, can.height );
ctx.fillStyle = "#000000"; ctx.fill();
document.body.appendChild( can );

ctx.fillStyle = "#ffffff";
for( var t = 0; t < 1000; t += .1 ) {
x = Math.pow( Math.abs( Math.cos( t ) ), 2 / n ) * a * Math.sign( Math.cos( t ) );
y = Math.pow( Math.abs( Math.sin( t ) ), 2 / n ) * b * Math.sign( Math.sin( t ) );

point( x + ( can.width >> 1 ), y + ( can.height >> 1 ) );
}
}



## Julia

{{works with|Julia|0.6}}

function superellipse(n, a, b, step::Int=100)
@assert n > 0 && a > 0 && b > 0
na = 2 / n
pc = 2π / step
t  = 0
xp = Vector{Float64}(step + 1)
yp = Vector{Float64}(step + 1)
for i in 0:step
# because sin^n(x) is mathematically the same as (sin(x))^n...
xp[i+1] = abs((cos(t))) ^ na * a * sign(cos(t))
yp[i+1] = abs((sin(t))) ^ na * b * sign(sin(t))
t += pc
end
return xp, yp
end

using UnicodePlots

x, y = superellipse(2.5, 200, 200)
println(lineplot(x, y))


{{out}}


┌────────────────────────────────────────┐
200 │⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠊⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠒⠒⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀│
│⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⠀⠀│
│⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀│
│⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆│
│⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱│
│⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸│
│⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼│
│⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸│
│⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸│
│⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇│
│⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀│
│⠀⠀⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀│
│⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀│
-200 │⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠤⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⡠⠤⠔⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀│
└────────────────────────────────────────┘
-200                                   200


## Kotlin

The following is based on the Java entry but dispenses with the grid and slider as these aren't really part of the task.

// version 1.1.2

import java.awt.*
import java.awt.geom.Path2D
import javax.swing.*
import java.lang.Math.pow

/* assumes a == b */
class SuperEllipse(val n: Double, val a: Int) : JPanel() {
init {
require(n > 0.0 && a > 0)
preferredSize = Dimension(650, 650)
background = Color.black
}

private fun drawEllipse(g: Graphics2D) {
val points = DoubleArray(a + 1)
val p = Path2D.Double()
p.moveTo(a.toDouble(), 0.0)

for (x in a downTo 0) {
points[x] = pow(pow(a.toDouble(), n) - pow(x.toDouble(), n), 1.0 / n)
p.lineTo(x.toDouble(), -points[x])
}

// mirror to others
for (x in 0..a) p.lineTo(x.toDouble(), points[x])
for (x in a downTo 0) p.lineTo(-x.toDouble(), points[x])
for (x in 0..a) p.lineTo(-x.toDouble(), -points[x])

with(g) {
translate(width / 2, height / 2)
color = Color.yellow
fill(p)
}
}

override fun paintComponent(gg: Graphics) {
super.paintComponent(gg)
val g = gg as Graphics2D
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON)
g.setRenderingHint(RenderingHints.KEY_TEXT_ANTIALIASING,
RenderingHints.VALUE_TEXT_ANTIALIAS_ON)
drawEllipse(g)
}
}

fun main(args: Array<String>) {
SwingUtilities.invokeLater {
val f = JFrame()
with (f) {
defaultCloseOperation = JFrame.EXIT_ON_CLOSE
title = "Super Ellipse"
isResizable = false
pack()
setLocationRelativeTo(null)
isVisible = true
}
}
}


## Maple

The built-in command ImplicitPlot accepts an equation in 2 variables:

plots:-implicitplot(abs((1/200)*x^2.5)+abs((1/200)*y^2.5) = 1, x = -10 .. 10, y = -10 .. 10);


## Mathematica

The built-in function ContourPlot accepts and equation in 2 variables and creates the desired plot

ContourPlot[
Abs[x/200]^2.5 + Abs[y/200]^2.5 == 1, {x, -200, 200}, {y, -200, 200}]


## ooRexx

This program draws 5 super ellipses:
black 120,120,1.5
blue  160,160,2
red   200,200,2.5
green 240,240,3
black 280,280,4

/* REXX ***************************************************************
* Create a BMP file showing a few super ellipses
**********************************************************************/
Parse Version v
If pos('Regina',v)>0 Then
superegg='superegga.bmp'
Else
superegg='supereggx.bmp'
'erase' superegg
s='424d4600000000000000360000002800000038000000280000000100180000000000'X||,
'1000000000000000000000000000000000000000'x
z.0=0
black='000000'x
white='ffffff'x
red  ='00ff00'x
green='ff0000'x
blue ='0000ff'x
m=80
n=80
hor=m*8      /* 56 */
ver=n*8      /* 40 */
s=overlay(lend(hor),s,19,4)
s=overlay(lend(ver),s,23,4)
z.=copies('f747ff'x,3192%3)
z.=copies('ffffff'x,8*m)
z.0=648
u=320
v=320
Call supegg black,120,120,1.5,u,v
Call supegg blue,160,160,2,u,v
Call supegg red,200,200,2.5,u,v
Call supegg green,240,240,3,u,v
Call supegg black,280,280,4,u,v

Do i=1 To z.0
s=s||z.i
End

Call lineout superegg,s
Call lineout superegg
Exit

supegg:
Parse Arg color,a,b,n,u,v
Do y=0 To b
t=(1-rxCalcpower(y/b,n))
x=a*rxCalcpower(t,1/n)
Call point color,format(u+x,4,0),format(v+y,4,0)
Call point color,format(u-x,4,0),format(v+y,4,0)
Call point color,format(u+x,4,0),format(v-y,4,0)
Call point color,format(u-x,4,0),format(v-y,4,0)
End
Do x=0 To a
t=(1-rxCalcpower(x/b,n))
y=a*rxCalcpower(t,1/n)
Call point color,format(u+x,4,0),format(v+y,4,0)
Call point color,format(u-x,4,0),format(v+y,4,0)
Call point color,format(u+x,4,0),format(v-y,4,0)
Call point color,format(u-x,4,0),format(v-y,4,0)
End
Return

lend:
Return reverse(d2c(arg(1),4))

point: Procedure Expose z.
Call trace 'O'
Parse Arg color,x0,y0
--Say x0 y0
Do x=x0-2 To x0+2
Do y=y0-2 To y0+2
z.y=overlay(copies(color,3),z.y,3*x)
End
End
Return

::requires rxMath library


## Perl

{{trans|Perl 6}}

my $a = 200; my$b = 200;
my $n = 2.5; # y in terms of x sub y_from_x { my($x) = @_;
int $b * abs(1 - ($x / $a) **$n ) ** (1/$n) } # find point pairs for one quadrant push @q,$_, y_from_x($_) for 0..200; # Generate an SVG image open$fh, '>', 'superellipse.svg';
print $fh qq|<svg height="@{[2*$b]}" width="@{[2*$a]}" xmlns="http://www.w3.org/2000/svg">\n|, pline( 1, 1, @q ), pline( 1,-1, @q ), # flip and mirror pline(-1,-1, @q ), # for the other pline(-1, 1, @q ), # three quadrants '</svg>'; sub pline { my($sx,$sy,@q) = @_; for (0..$#q/2) {
$q[ 2*$_] *= $sx;$q[1+2*$_] *=$sy;
}

qq|<polyline points="@{[join ' ',@q]}"
style="fill:none;stroke:black;stroke-width:3"
transform="translate($a,$b)" />\n|
}


[https://github.com/SqrtNegInf/Rosettacode-Perl5-Smoke/blob/master/ref/superellipse.svg Superellipse] (offsite image)

## Perl 6

{{works with|rakudo|2018-10}} Generate an svg image to STDOUT. Redirect into a file to capture it.

constant a = 200;
constant b = 200;
constant n = 2.5;

# y in terms of x
sub y ($x) { sprintf "%d", b * (1 - ($x / a).abs ** n ) ** (1/n) }

# find point pairs for one quadrant
my @q = flat map -> \x { x, y(x) }, (0, 1 ... 200);

# Generate an SVG image
INIT say qq:to/STOP/;
<?xml version="1.0" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg height="{b*2}" width="{a*2}" version="1.1" xmlns="http://www.w3.org/2000/svg">
STOP
END say '</svg>';

.put for
pline( @q ),
pline( @q «*» ( 1,-1) ), # flip and mirror
pline( @q «*» (-1,-1) ), # for the other
pline( @q «*» (-1, 1) ); # three quadrants

sub pline (@q) {
qq:to/END/;
<polyline points="{@q}"
style="fill:none; stroke:black; stroke-width:3" transform="translate({a}, {b})" />
END
}


[https://github.com/SqrtNegInf/Rosettacode-Perl6-Smoke/blob/master/ref/superellipse.svg Superellipse] (offsite image)

## Phix

-- demo\rosetta\Superellipse.exw
atom n = 2.5        -- '+' and '-' increase/decrease in steps of 0.1
integer a = 200,    -- resize window to set this from canvas width
b = 200     -- resize window to set this from canvas height

include pGUI.e

Ihandle dlg, canvas
cdCanvas cddbuffer, cdcanvas

function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)

integer {hw, hh} = sq_floor_div(IupGetIntInt(canvas, "DRAWSIZE"),2)
a = max(10,hw-100)  -- (initially 200, from 602x   )
b = max(10,hh-50)   -- (initially 200, from    x502)
sequence y = b&repeat(0,a)
for x=1 to a-1 do
y[x+1] = floor(exp(log(1-power(x/a,n))/n)*b)
end for

cdCanvasActivate(cddbuffer)
cdCanvasClear(cddbuffer)
cdCanvasBegin(cddbuffer, CD_OPEN_LINES)
cdCanvasVertex(cddbuffer, hw, hh-b) -- starting point
for x=1 to a-1     do cdCanvasVertex(cddbuffer, hw+x, hh-y[x+1]) end for
for x=a to 0 by -1 do cdCanvasVertex(cddbuffer, hw+x, hh+y[x+1]) end for
for x=0 to a       do cdCanvasVertex(cddbuffer, hw-x, hh+y[x+1]) end for
for x=a to 0 by -1 do cdCanvasVertex(cddbuffer, hw-x, hh-y[x+1]) end for
cdCanvasEnd(cddbuffer)
cdCanvasFlush(cddbuffer)

return IUP_DEFAULT
end function

function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih)
cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
cdCanvasSetBackground(cddbuffer, CD_WHITE)
cdCanvasSetForeground(cddbuffer, CD_BLACK)
return IUP_DEFAULT
end function

function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if
if c='+' then
n = min(130,n+0.1) -- (otherwise [>130] power overflow)
IupUpdate(canvas)
elsif c='-' then
n = max(0.1,n-0.1) -- (otherwise [=0.0] divide by zero)
IupUpdate(canvas)
end if
return IUP_CONTINUE
end function

procedure main()
IupOpen()

canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "602x502") -- initial size
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))

dlg = IupDialog(canvas)
IupSetAttribute(dlg, "TITLE", "Superellipse")
IupSetCallback(dlg, "K_ANY",     Icallback("esc_close"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))

IupMap(dlg)
IupSetAttribute(canvas, "RASTERSIZE", NULL) -- release the minimum limitation
IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
IupMainLoop()
IupClose()
end procedure
main()


## Python


# Superellipse drawing in Python 2.7.9
# pic can see at http://www.imgup.cz/image/712

import matplotlib.pyplot as plt
from math import sin, cos, pi

def sgn(x):
return ((x>0)-(x<0))*1

a,b,n=200,200,2.5 # param n making shape
na=2/n
step=100 # accuracy
piece=(pi*2)/step
xp=[];yp=[]

t=0
for t1 in range(step+1):
# because sin^n(x) is mathematically the same as (sin(x))^n...
x=(abs((cos(t)))**na)*a*sgn(cos(t))
y=(abs((sin(t)))**na)*b*sgn(sin(t))
xp.append(x);yp.append(y)
t+=piece

plt.plot(xp,yp) # plotting all point from array xp, yp
plt.title("Superellipse with parameter "+str(n))
plt.show()



## Racket

#lang racket
(require plot)
#;(plot-new-window? #t)

(define ((superellipse a b n) x y)
(+ (expt (abs (/ x a)) n)
(expt (abs (/ y b)) n)))

(plot (isoline (superellipse 200 200 2.5) 1
-220 220 -220 220))


## REXX

{{trans|ooRexx}} Here you can see a picture: http://austria-forum.org/af/User/Pachl%20Walter

/* REXX ***************************************************************
* Create a BMP file showing a few super ellipses
**********************************************************************/
Parse Version v
If pos('Regina',v)>0 Then
superegg='superegga.bmp'
Else
superegg='supereggo.bmp'
'erase' superegg
s='424d4600000000000000360000002800000038000000280000000100180000000000'X||,
'1000000000000000000000000000000000000000'x
z.0=0
black='000000'x
white='ffffff'x
red  ='00ff00'x
green='ff0000'x
blue ='0000ff'x
m=80
n=80
hor=m*8      /* 56 */
ver=n*8      /* 40 */
s=overlay(lend(hor),s,19,4)
s=overlay(lend(ver),s,23,4)
z.=copies('f747ff'x,3192%3)
z.=copies('ffffff'x,8*m)
z.0=648
u=320
v=320
Call supegg black,080,080,0.5,u,v
Call supegg black,110,110,1 ,u,v
Call supegg black,140,140,1.5,u,v
Call supegg blue ,170,170,2 ,u,v
Call supegg red ,200,200,2.5,u,v
Call supegg green,230,230,3 ,u,v
Call supegg black,260,260,4 ,u,v
Call supegg black,290,290,7 ,u,v
Do i=1 To z.0
s=s||z.i
End

Call lineout superegg,s
Call lineout superegg
Exit

supegg:
Parse Arg color,a,b,n,u,v
Do y=0 To b
t=(1-power(y/b,n))
x=a*power(t,1/n)
Call point color,format(u+x,4,0),format(v+y,4,0)
Call point color,format(u-x,4,0),format(v+y,4,0)
Call point color,format(u+x,4,0),format(v-y,4,0)
Call point color,format(u-x,4,0),format(v-y,4,0)
End
Do x=0 To a
t=(1-power(x/b,n))
y=a*power(t,1/n)
Call point color,format(u+x,4,0),format(v+y,4,0)
Call point color,format(u-x,4,0),format(v+y,4,0)
Call point color,format(u+x,4,0),format(v-y,4,0)
Call point color,format(u-x,4,0),format(v-y,4,0)
End
Return

lend:
Return reverse(d2c(arg(1),4))

point: Procedure Expose z.
Call trace 'O'
Parse Arg color,x0,y0
--Say x0 y0
Do x=x0-2 To x0+2
Do y=y0-2 To y0+2
z.y=overlay(copies(color,3),z.y,3*x)
End
End
Return

power: Procedure
/***********************************************************************
* Return b**x for any x -- with reasonable or specified precision
* 920903 Walter Pachl
***********************************************************************/
Parse Arg b,x,prec
If prec<9 Then prec=9
Numeric Digits (2*prec)
Numeric Fuzz   3
If b=0 Then Return 0
If b<>'' Then x=x*ln(b,prec+2)
o=1
u=1
r=1
Do i=1 By 1
ra=r
o=o*x
u=u*i
r=r+(o/u)
If r=ra Then Leave
End
Numeric Digits (prec)
Return r+0

ln: Procedure
/***********************************************************************
* Return ln(x) -- with specified precision
* Three different series are used for the ranges  0 to 0.5
*                                                 0.5 to 1.5
*                                                 1.5 to infinity
* 920903 Walter Pachl
***********************************************************************/
Parse Arg x,prec,b
If prec='' Then prec=9
Numeric Digits (2*prec)
Numeric Fuzz   3
Select
When x<=0 Then r='*** invalid argument ***'
When x<0.5 Then Do
z=(x-1)/(x+1)
o=z
r=z
k=1
Do i=3 By 2
ra=r
k=k+1
o=o*z*z
r=r+o/i
If r=ra Then Leave
End
r=2*r
End
When x<1.5 Then Do
z=(x-1)
o=z
r=z
k=1
Do i=2 By 1
ra=r
k=k+1
o=-o*z
r=r+o/i
If r=ra Then Leave
End
End
Otherwise /* 1.5<=x */ Do
z=(x+1)/(x-1)
o=1/z
r=o
k=1
Do i=3 By 2
ra=r
k=k+1
o=o/(z*z)
r=r+o/i
If r=ra Then Leave
End
r=2*r
End
End
If b<>'' Then
r=r/ln(b)
Numeric Digits (prec)
Return r+0


## Scala

### Java Swing Interoperability

import java.awt._
import java.awt.geom.Path2D
import java.util

import javax.swing._
import javax.swing.event.{ChangeEvent, ChangeListener}

object SuperEllipse extends App {

SwingUtilities.invokeLater(() => {
new JFrame("Super Ellipse") {

class SuperEllipse extends JPanel with ChangeListener {
setPreferredSize(new Dimension(650, 650))
setBackground(Color.white)
setFont(new Font("Serif", Font.PLAIN, 18))
private var exp = 2.5

override def paintComponent(gg: Graphics): Unit = {
val g = gg.asInstanceOf[Graphics2D]

def drawGrid(g: Graphics2D): Unit = {
g.setStroke(new BasicStroke(2))
g.setColor(new Color(0xEEEEEE))
val w = getWidth
val h = getHeight
val spacing = 25

for (i <- 0 until (w / spacing)) {
g.drawLine(0, i * spacing, w, i * spacing)
g.drawLine(i * spacing, 0, i * spacing, w)
}
g.drawLine(0, h - 1, w, h - 1)
g.setColor(new Color(0xAAAAAA))
g.drawLine(0, w / 2, w, w / 2)
g.drawLine(w / 2, 0, w / 2, w)
}

def drawLegend(g: Graphics2D): Unit = {
g.setColor(Color.black)
g.setFont(getFont)
g.drawString("n = " + String.valueOf(exp), getWidth - 150, 45)
g.drawString("a = b = 200", getWidth - 150, 75)
}

def drawEllipse(g: Graphics2D): Unit = {
val a = 200
val points = Array.tabulate(a + 1)(n =>
math.pow(math.pow(a, exp) - math.pow(n, exp), 1 / exp))
val p = new Path2D.Double

p.moveTo(a, 0)
for (n <- a to 0 by -1) p.lineTo(n, -points(n))
// mirror to others
for (x <- points.indices) p.lineTo(x, points(x))
for (y <- a to 0 by -1) p.lineTo(-y, points(y))
for (z <- points.indices) p.lineTo(-z, -points(z))
g.translate(getWidth / 2, getHeight / 2)
g.setStroke(new BasicStroke(2))
g.setColor(new Color(0x25B0C4DE, true))
g.fill(p)
g.setColor(new Color(0xB0C4DE)) // LightSteelBlue
g.draw(p)
}

super.paintComponent(gg)
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
g.setRenderingHint(RenderingHints.KEY_TEXT_ANTIALIASING, RenderingHints.VALUE_TEXT_ANTIALIAS_ON)
drawGrid(g)
drawLegend(g)
drawEllipse(g)
}

override def stateChanged(e: ChangeEvent): Unit = {
val source = e.getSource.asInstanceOf[JSlider]
exp = source.getValue / 2.0
repaint()
}
}

setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE)
setResizable(false)
val panel = new SuperEllipse
val exponent = new JSlider(SwingConstants.HORIZONTAL, 1, 9, 5)
exponent.setBackground(Color.white)
exponent.setBorder(BorderFactory.createEmptyBorder(20, 20, 20, 20))
exponent.setMajorTickSpacing(1)
exponent.setPaintLabels(true)
val labelTable = new util.Hashtable[Integer, JLabel]
for (i <- 1 until 10) labelTable.put(i, new JLabel(String.valueOf(i * 0.5)))

exponent.setLabelTable(labelTable)
pack()
setLocationRelativeTo(null)
setVisible(true)
}

})

}


## Sidef

{{trans|Perl 6}}

const (
a = 200,
b = 200,
n = 2.5,
)

# y in terms of x
func y(x) { b * (1 - abs(x/a)**n -> root(n)) -> int }

func pline(q) {
<<-"EOT";
<polyline points="#{q.join(' ')}"
style="fill:none; stroke:black; stroke-width:3" transform="translate(#{a}, #{b})" />
EOT
}

# Generate an SVG image
say <<-"EOT"
<?xml version="1.0" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg height="#{b*2}" width="#{a*2}" version="1.1" xmlns="http://www.w3.org/2000/svg">
EOT

# find point pairs for one quadrant
var q = { |x| (x, y(x)) }.map(0..200 by 2)

[
pline(q),
pline(q »*« [ 1,-1]), # flip and mirror
pline(q »*« [-1,-1]), # for the other
pline(q »*« [-1, 1]), # three quadrants
].each { .print }

say '</svg>'


## Stata

sca a=200
sca b=200
sca n=2.5
twoway function y=b*(1-(abs(x/a))^n)^(1/n), range(-200 200) || function y=-b*(1-(abs(x/a))^n)^(1/n), range(-200 200)


## zkl

Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl [[File:SuperEllipse.zkl.jpg|250px|thumb|right]]

fcn superEllipse(plot,n,color=0xff0000){ // we'll assume width <= height
a,p:=(plot.w/2).toFloat(), 1.0/n;  // just calculate upper right quadrant
foreach x in ([0.0 .. a]){
y:=(a.pow(n) - x.pow(n)).pow(p);  // a==b>0 --> y=(a^n - x^n)^(1/n)
//println( (x/a).abs().pow(n) + (y/b).abs().pow(n) );  // sanity check

w:=h:=600;