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Last active February 2, 2016 10:56
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[JAVASCRIPT] How to cover a rectangle with a circle when the circle's center is not at the same position as the rectangle's center
<!DOCTYPE html>
<meta charset="UTF-8">
<title>Circle in rectangle</title>
By Dani Guardiola
The diameter() function calculates the diameter that a circle
must have to cover a rectangle based on its center position and
the rectangle's dimensions.
The run() function reflects it into the DOM for demonstration purposes.
Further explanation:
Imagine that we want to cover a rectangle completely with a circle with
the same center as the rectangle. To find the correct diameter in this
case, we just have to calculate the diagonal of the rectangle and use it
as the circle's diameter.
This is very easy to calculate just by using the Pythagoras' Theorem:
outer_radius = 0.5 * sqrt(width * width + height * height)
But what happens when the center of the circle is not at the same
position as the center of the rectangle?
Well in that case, we must readjust the width and the height used to
calculate the radius by "simulating" another rectangle with the same
center position as the circle.
The way to do this is simple, we just have to find out what distance to
the edge from the circle center position is greater in X and Y, and
duplicate it to find out the new rectangle dimensions.
For example, to find out the width of the new rectangle, we must first
find the distance from X to the left edge (which is X itself) and to
the right edge (initial width minus X).
Then we duplicate the greater value of those two and we have the width
we are gonna use to calculate the radius of the circle.
<div id="rectangle" style="margin: 150px; height: 100px; width: 100px; background-color: blue; position: relative;">
<div id="circle" style="border-radius: 50%; height: 50px; width: 50px; background-color: rgba(0, 0, 0, 0.5); top: 25px; left: 25px; position: absolute;"></div>
<script type="text/javascript">
function run(x, y) {
var rectangle = document.querySelector("#rectangle");
var circle = document.querySelector("#circle");
var rect = rectangle.getBoundingClientRect();
var d = diameter(rect.width, rect.height, x, y); = = d + "px"; = y - (d / 2) + "px"; = x - (d / 2) + "px";
function diameter(w, h, x, y) {
var width = Math.max(w - x, x) * 2;
var height = Math.max(h - y, y) * 2;
var diameter = Math.sqrt(width * width + height * height);
return diameter;
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