Hit testing pseudo 3d space

So I am writing a little mini pseudo 3d engine for the canvas element in html5. In the code below I am drawing a bunch of squares with varying positions and rotations (rot开发者_StackOverflowation around the z axis, so no deformation)

Now I want to be able to tell which square the user clicks on. In the objects array the items are supported by the z position starting with the squares the furthest away from the camera (so that they draw properly). So given a 3d point relative to the top left of the corner of the canvas how can I tell which square was clicked?

//Draw objects
for (var i = 0; i < objects.length; i++) {
    var object = objects[i];
    var cz = object.position.z - camera.position.z;

    if (cz > 0) {
        cz = 1 / ((cz - 1) * 0.75 + 1);

        context.save();

        context.translate(halfWidth, halfHeight); //viewport transform
        context.scale(1, -1); //invert y axis
        context.scale(cz, cz); //perspective
        context.translate(-camera.position.x, -camera.position.y); //camera transform
        context.translate(object.position.x, object.position.y); //world transform
        context.rotate(object.rotation);

        context.fillStyle = object.color;
        context.fillRect(-40, -40, 80, 80);

        context.restore();
    }
}

P.S. If I am doing anything weird or backwards and you know of a way to improve, I would love to hear suggestions

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I would suggest that you draw the objects with the same transformations to a hidden canvas of the same size, but give each square a unique color (maybe derived from the index i).

You would do that like this:

var col = index.toString(16);                 // convert to hex
while (col.length < 6) col = "0"+col;     // pad leading 0s
ctx.fillStyle = "#"+col;
ctx.fillRect(-40,-40,80,80);

Then when you get a mouseclick event on the visible canvas, look at that location in your hidden one to get the color (index) of the selected object:

var colData = ctx.getImageData(clickX, clickY, 1, 1).data;
var index = (colData[2]<<16) | (colData[1]<<8) | colData[0];

This will work for up to 16M objects and is fairly simple.