Drawing an ellipse outside rectangle, what is the math for this?

Drawing an ellipse outside rectangle, what is the math for this?

I drew a rectangle, and now I want to draw an ellipse outside it so that rectangle fits barely inside the ellipse.

I don't want a perfect circle around the rectangle, that I can do with diagonal length.

I want an ellipse, just barely going around the corners of the rectangle.

Here's my code, and edges of the rectangle are stretching outside the ellipse.
How can I fix this?

If the ellipse is slightly larger than the rectangle, even that is ok,
but must work for rectangle of any proportions.

<?php

$width=500; $height=300;
$im= imagecreatetruecolor( $width, $height );
$b= imagecolorallocate($im, 0, 0, 0);
$w= imagecolorallocate($im, 255, 255, 255);
imagefill($im, 0,0, $b);


$x=($width/2)-75;
$y=($height/2)-25;
$x1=($width/2)+75;
$y1=($height/2)+25;

imagerectangle($im, $x,$y, $x1,$y1, $w);



//try some ratios

$x= ($x1-$x);
$y=($y1-$y);
$ratio= ceil($x/$y);
//echo "$x = $y = $ratio";exit;

$x=$x+ ceil($x/$ratio);
$y=$y+ ceil($y/$ratio);

//draw the ellipse around the rectangle
imageellipse($im, ($width/2), ($height/2),
$x,$y,
$w);


header("Content-Type: image/png");
imagepng($im);
?>

 

Hi.
I don't understand how you get lines, after

Perhaps you should derive first the basic equation of an ellipse:
https://www.mathsisfun.com/geometry/ellipse.html#equation

x**2 / a**2 + y**2 / b**2 = 1
(where a = half of ellipse width and b = half of ellipse height)

If we know ratio of a / b then logically the value of a can be solved.
FYI you can use any corners of rectangle for values of x and y.

So i guess your code becomes like the following:

<?php

$width=500; $height=300;
$im= imagecreatetruecolor( $width, $height );
$b= imagecolorallocate($im, 0, 0, 0);
$w= imagecolorallocate($im, 255, 255, 255);
imagefill($im, 0,0, $b);


//rectangle
$x=($width/2)-75;
$y=($height/2)-25;
$x1=($width/2)+75;
$y1=($height/2)+25;

imagerectangle($im, $x,$y, $x1,$y1, $w);


//ellipse center
$ellcx = ($x + $x1) / 2;
$ellcy = ($y + $y1) / 2;

//ellipse height / width
$ellh2wratio = 0.3;

//ellipse width
$ellw = 2 * sqrt(($x - $ellcx)**2 + ($y - $ellcy)**2 / $ellh2wratio**2);

//ellipse height
$ellh = $ellh2wratio * $ellw;

//draw the ellipse around the rectangle
imageellipse($im, $ellcx, $ellcy, $ellw, $ellh, $w);


header("Content-Type: image/png");
imagepng($im);
?> 

PHP:

 

Thanks for replying.
How did you get this ellipse ratio? Is this constant, or is it the ratio width and height of rectangle?
$ellh2wratio = 0.3;

Also, this line doesn't seems right.
//ellipse width
$ellw = 2 * sqrt(($x - $ellcx)*2 + ($y - $ellcy)*2 / $ellh2wratio*2);


I also get parse error because of double * signs.

 

It's the ratio of height to width of your ellipse and the value is up to you. For example:
$ellh2wratio = 0.3 creates flat ellipse.
$ellh2wratio = 1 makes perfect circle

** is the same as pow()

$ellw = 2 * sqrt(($x - $ellcx)**2 + ($y - $ellcy)**2 / $ellh2wratio**2);

PHP:

of if you rather use pow() for php < 5.6:

$ellw = 2 * sqrt(pow($x - $ellcx,2) + pow($y - $ellcy,2) / pow($ellh2wratio,2));

PHP:

I derived it by hand from: x^2/a^2 + y^2/b^2 = 1
(see article in https://www.mathsisfun.com/geometry/ellipse.html#equation)

 

@hdewantara
This is brilliant! Many thanks for this!

 

am pleased to help