Map translated coordinates back to original - algorithm

Question

Once a transformation of coordinates has taken place during a the rendering of a computer graphics scene, how do you map inputs on the rendered scene back to the original actor(s) coordinate systems?
Using this JSFiddle https://jsfiddle.net/bbz5s183/3/ as a starting point, implement the canvas click event handler so that.
It can identify if a star was clicked.
It will work consistently no matter how the canvas is resized.
JSFIDDLE SCRIPT CONTENT BELOW
var draggable = document.getElementById('draggable')
var canvas = document.getElementById('canvas');
var context = canvas.getContext('2d');
// Draw a star in a 1 x 1 coordinate plane.
function star(color) {
context.beginPath();
context.moveTo(0.5, 0);
context.lineTo(0.15, 1.0);
context.lineTo(1.0, 0.4);
context.lineTo(0, 0.4);
context.lineTo(0.85, 1.0);
context.closePath();
context.fillStyle = color;
context.fill();
}
// Draw a scene of stars in a coordinate plane defined by the canvas.
// This is initially 300 x 300, but can be resized to anything by dragging the gray border.
function render() {
context.setTransform(1, 0, 0, 1, 0, 0);
context.translate(canvas.width / 2, canvas.height / 2);
context.scale(canvas.width / 5, canvas.height / 5);
star('red');
context.setTransform(1, 0, 0, 1, 0, 0);
context.translate(canvas.width / 4, canvas.height / 4);
context.scale(canvas.width / 5, canvas.height / 5);
star('yellow');
}
// Pop an alert indicating which star (if any) was clicked on.
// NOTE: The logic MUST work consistently no matter how the canvas is resized.
canvas.addEventListener('click', function (event) {
event.stopImmediatePropagation();
// HELP ME !!!
// HELP ME !!!
// HELP ME !!!
// HELP ME !!!
});
// IGNORE: It allows the canvas to resized by dragging on it.
draggable.addEventListener('mousedown', function handleMouseDown(mousedown) {
document.addEventListener('mouseup', function handleMouseUp(mouseup) {
var currWidth = Number(canvas.getAttribute('width'));
var deltaWidth = mouseup.clientX - mousedown.clientX;
var currHeight = Number(canvas.getAttribute('height'));
var deltaHeight = mouseup.clientY - mousedown.clientY;
canvas.setAttribute('width', currWidth + deltaWidth);
canvas.setAttribute('height', currHeight + deltaHeight);
document.removeEventListener('mouseup', handleMouseUp);
render();
});
});
render();

Answer 1

Answered my own question: https://jsfiddle.net/bbz5s183/4/
JAVASCRIPT FOLLOWS
// Draw a scene of stars in a coordinate plane defined by the canvas.
// This is initially 300 x 300, but can be resized to anything by dragging the gray border.
function render() {
bounds = [];
/* RENDER RED ACTOR - BOUNDING BOX */
var red = {
name: 'red',
// Translate to 25% right, 25% down on canvas.
x: 0.25 * canvas.width,
y: 0.25 * canvas.height,
// Scale to fill 20% of canvas.
width: 0.2 * canvas.width,
height: 0.2 * canvas.height
};
context.setTransform(1, 0, 0, 1, 0, 0);
box('red', red);
bounds.push(red);
/* RENDER RED ACTOR - MODEL */
context.setTransform(1, 0, 0, 1, 0, 0);
context.translate(red.x, red.y);
context.scale(red.width, red.height);
star('red');
/* RENDER YELLOW ACTOR - BOUNDING BOX */
var yellow = {
name: 'yellow',
// Translate to 50% right, 50% down on canvas.
x: 0.50 * canvas.width,
y: 0.50 * canvas.height,
// Scale to fill 20% of canvas.
width: 0.2 * canvas.width,
height: 0.2 * canvas.height
};
context.setTransform(1, 0, 0, 1, 0, 0);
box('yellow', yellow);
bounds.push(yellow);
/* RENDER YELLOW ACTOR - MODEL */
context.setTransform(1, 0, 0, 1, 0, 0);
context.translate(yellow.x, yellow.y);
context.scale(yellow.width, yellow.height);
star('yellow');
}
// Pop an alert indicating which star (if any) was clicked on.
// NOTE: The logic MUST work consistently no matter how the canvas is resized.
canvas.addEventListener('click', function (event) {
var x = event.pageX - event.target.offsetLeft;
var y = event.pageY - event.target.offsetTop;
for (var i = 0; i < bounds.length; i++) {
if (boxIntersection(bounds[i], x, y)) {
alert(bounds[i].name);
};
}
event.stopImmediatePropagation();
return false;
});