HTML Canvas, mouse position after scale and translate

Question

I implemented a zoom function in my canvas just like this one: Zoom in on a point (using scale and translate)

Now I need to calculate the position of the mouse in relation to the canvas, I first tried like this:

var rect = this._canvas.getBoundingClientRect();
var x = ((event.clientX  - rect.left) / (rect.right - rect.left) * this._canvas.width);
var y = ((event.clientY  - rect.top) / (rect.bottom  - rect.top) * this._canvas.height);

This works excellent until I zoom... I tried to do it like this:

var x = ((event.clientX  - rect.left) / (rect.right - rect.left) * this._canvas.width) - this._canvas.offsetLeft ;
var y = ((event.clientY  - rect.top) / (rect.bottom  - rect.top) * this._canvas.height) - offset.top this._canvas.offSetTop ;

Any hint ? Or should I better use a JS library to interact with the canvas element ? If so, do you have any experience ?

Answer 1

Inverse Matrix

This answer include rotation as well because the scale is part of the rotation in the matrix you can't really exclude one or the other. But you can ignore the rotation (set it as zero) and just set scale and translation and it does what you want.

The inverse transform. It basically does the reverse of the standard 2D transformations. It will require that you keep track of the transformations so you can create the inverse transform, this can prove problematic in complex transforms if you wish to use ctx.rotation, ctx.scale, ctx.translate or ctx.transform. As you requirements are simple I have created a simple function to do the minimum transformation.

The following creates both the transformation matrix and the inverse transform as two arrays called matrix and invMatrix. The arguments are translation x,y (in canvas coordinates), scale, and rotation.

var matrix = [1,0,0,1,0,0];
var invMatrix = [1,0,0,1];
function createMatrix(x, y, scale, rotate){
    var m = matrix; // just to make it easier to type and read
    var im = invMatrix; // just to make it easier to type and read

    // create the rotation and scale parts of the matrix
    m[3] =   m[0] = Math.cos(rotate) * scale;
    m[2] = -(m[1] = Math.sin(rotate) * scale);

    // add the translation
    m[4] = x;
    m[5] = y;

    // calculate the inverse transformation

    // first get the cross product of x axis and y axis
    cross = m[0] * m[3] - m[1] * m[2];

    // now get the inverted axis
    im[0] =  m[3] / cross;
    im[1] = -m[1] / cross;
    im[2] = -m[2] / cross;
    im[3] =  m[0] / cross;
 }  

Using the function

To use the function is simple. Just call with the desired values for position, scale and rotation.

Applying the inverse

To get the world coordinates (the transformed coordinates) from a pixel space (screen x, y) you need to apply the inverse transform

function toWorld(x,y){        
    var xx, yy, m, result;
    m = invMatrix;
    xx = x - matrix[4];     // remove the translation 
    yy = y - matrix[5];     // by subtracting the origin
    // return the point {x:?,y:?} by multiplying xx,yy by the inverse matrix
    return {
       x:   xx * m[0] + yy * m[2],
       y:   xx * m[1] + yy * m[3]
    }
}

So if you want the mouse position in world space

var mouseWorldSpace = toWorld(mouse.x,mouse.y);  // get the world space coordinates of the mouse

The function will convert any coordinate that is in screen space to the correct coordinate in world space.

Setting the 2D context transform

To use the transform you can set the 2D context transformation directly with

var m = matrix;
ctx.setTransform(m[0], m[1], m[2], m[3], m[4], m[5]);

Demo

And a demo to show it in use. A lot of extra code but I am sure you can find the parts you need. The Demo animates the transformation by rotating, scaling, and translating using createMatrix then uses toWorld to convert the mouse coordinates to the world space.

// the demo function

var demo = function(){
    /** fullScreenCanvas.js begin **/
    // create a full document canvas on top 
    var canvas = (function(){
        var canvas = document.getElementById("canv");
        if(canvas !== null){
            document.body.removeChild(canvas);
        }
        // creates a blank image with 2d context
        canvas = document.createElement("canvas"); 
        canvas.id = "canv";    
        canvas.width = window.innerWidth;
        canvas.height = window.innerHeight; 
        canvas.style.position = "absolute";
        canvas.style.top = "0px";
        canvas.style.left = "0px";
        canvas.style.zIndex = 1000;
        canvas.ctx = canvas.getContext("2d"); 
        document.body.appendChild(canvas);
        return canvas;
    })();
    var ctx = canvas.ctx;
    
    /** fullScreenCanvas.js end **/
    /** MouseFull.js begin **/
    // get the mouse data . This is a generic mouse handler I use  so a little over kill for this example
    var canvasMouseCallBack = undefined;  // if needed
    var mouse = (function(){
        var mouse = {
            x : 0, y : 0, w : 0, alt : false, shift : false, ctrl : false,
            interfaceId : 0, buttonLastRaw : 0,  buttonRaw : 0,
            over : false,  // mouse is over the element
            bm : [1, 2, 4, 6, 5, 3], // masks for setting and clearing button raw bits;
            getInterfaceId : function () { return this.interfaceId++; }, // For UI functions
            startMouse:undefined,
        };
        function mouseMove(e) {
            var t = e.type, m = mouse;
            m.x = e.offsetX; m.y = e.offsetY;
            if (m.x === undefined) { m.x = e.clientX; m.y = e.clientY; }
            m.alt = e.altKey;m.shift = e.shiftKey;m.ctrl = e.ctrlKey;
            if (t === "mousedown") { m.buttonRaw |= m.bm[e.which-1];
            } else if (t === "mouseup") { m.buttonRaw &= m.bm[e.which + 2];
            } else if (t === "mouseout") { m.buttonRaw = 0; m.over = false;
            } else if (t === "mouseover") { m.over = true;
            } else if (t === "mousewheel") { m.w = e.wheelDelta;
            } else if (t === "DOMMouseScroll") { m.w = -e.detail;}
            if (canvasMouseCallBack) { canvasMouseCallBack(m.x, m.y); }
            e.preventDefault();
        }
        function startMouse(element){
            if(element === undefined){
                element = document;
            }
            "mousemove,mousedown,mouseup,mouseout,mouseover,mousewheel,DOMMouseScroll".split(",").forEach(
            function(n){element.addEventListener(n, mouseMove);});
            element.addEventListener("contextmenu", function (e) {e.preventDefault();}, false);
        }
        mouse.mouseStart = startMouse;
        return mouse;
    })();
    if(typeof canvas === "undefined"){
        mouse.mouseStart();
    }else{
        mouse.mouseStart(canvas);
    }
    /** MouseFull.js end **/
    
    
    // some stuff to draw a grid
    var gridStart= -(canvas.width/10)*4;
    var gridEnd = (canvas.width/10)*14;
    var gridStepMajor = canvas.width/10;
    var gridStepMinor = canvas.width/20;
    var minorCol = "#999";
    var majorCol = "#000";
    var minorWidth = 1;
    var majorWidth = 3;
    
    // some stuf to animate the transformation
    var timer = 0;
    var timerStep = 0.01;
 
 
    //----------------------------------------------------------------------------
    // the code from the answer
    var matrix = [1, 0, 0, 1, 0, 0];      // normal matrix
    var invMatrix = [1, 0, 0, 1];   // inverse matrix
    function createMatrix(x, y, scale, rotate){
        var m = matrix; // just to make it easier to type and read
        var im = invMatrix; // just to make it easier to type and read
        // create the scale and rotation part of the matrix
        m[3] =   m[0] = Math.cos(rotate) * scale;
        m[2] = -(m[1] = Math.sin(rotate) * scale);
        // translation
        m[4] = x;
        m[5] = y;
        
        // calculate the inverse transformation
        // first get the cross product of x axis and y axis
        cross = m[0] * m[3] - m[1] * m[2];
        // now get the inverted axies
        im[0] =  m[3] / cross;
        im[1] = -m[1] / cross;
        im[2] = -m[2] / cross;
        im[3] =  m[0] / cross;
     }  

    // function to transform to world space
    function toWorld(x,y){
        var xx, yy, m;
        m = invMatrix;
        xx = x - matrix[4];     
        yy = y - matrix[5];     
        return {
           x:   xx * m[0] + yy * m[2] ,
           y:   xx * m[1] + yy * m[3]
        }
    }
    //----------------------------------------------------------------------------


    // center of canvas    
    var cw = canvas.width / 2;
    var ch = canvas.height / 2;
   

    // the main loop
    function update(){
        var i,x,y,s;
        ctx.setTransform(1, 0, 0, 1, 0, 0);  // reset the transform so we can clear
        ctx.clearRect(0, 0, canvas.width, canvas.height);  // clear the canvas
        
        
        // animate the transformation
        timer += timerStep;
        x = Math.cos(timer) * gridStepMajor * 5 + cw;  // position
        y = Math.sin(timer) * gridStepMajor * 5 + ch;   
        s = Math.sin(timer/1.2) + 1.5;            // scale
        
        
        //----------------------------------------------------------------------
        // create the matrix at x,y scale = s and rotation time/3
        createMatrix(x,y,s,timer/3);      
        
        // use the created matrix to set the transformation
        var m = matrix;
        ctx.setTransform(m[0], m[1], m[2], m[3], m[4], m[5]);
        //----------------------------------------------------------------------------
        
        
        
        //draw a grid
        ctx.lineWidth = 2;
        ctx.beginPath();
        ctx.strokeStyle = majorCol ;
        ctx.lineWidth = majorWidth;
        for(i = gridStart; i <= gridEnd; i+= gridStepMajor){
            ctx.moveTo(gridStart, i);
            ctx.lineTo(gridEnd, i);
            ctx.moveTo(i, gridStart);
            ctx.lineTo(i, gridEnd);
        }
        ctx.stroke();
        ctx.strokeStyle = minorCol ;
        ctx.lineWidth = minorWidth;
        for(i = gridStart+gridStepMinor; i < gridEnd; i+= gridStepMinor){
            ctx.moveTo(gridStart, i);
            ctx.lineTo(gridEnd, i);
            ctx.moveTo(i, gridStart);
            ctx.lineTo(i, gridEnd);
        }
        ctx.stroke();
        
        //---------------------------------------------------------------------
        // get the mouse world coordinates
        var mouseWorldPos = toWorld(mouse.x, mouse.y);
        //---------------------------------------------------------------------
        
        
        // marke the location with a cross and a circle;
        ctx.strokeStyle = "red";
        ctx.lineWidth = 3;
        ctx.beginPath();
        ctx.moveTo(mouseWorldPos.x - gridStepMajor, mouseWorldPos.y)
        ctx.lineTo(mouseWorldPos.x + gridStepMajor, mouseWorldPos.y)
        ctx.moveTo(mouseWorldPos.x, mouseWorldPos.y - gridStepMajor)
        ctx.lineTo(mouseWorldPos.x, mouseWorldPos.y + gridStepMajor)
        ctx.stroke();
        
        
        ctx.fillStyle = "red";
        ctx.strokeStyle = "yellow";
        ctx.lineWidth = 4;
        ctx.beginPath();
        ctx.arc(mouseWorldPos.x, mouseWorldPos.y, 6, 0, Math.PI*2);
        ctx.fill();
        ctx.stroke();
        ctx.fillStyle = "Blue";
        ctx.setTransform(1,0,0,1,0,0);

        ctx.font = "18px Arial";
        var str = "Mouse canvas X: "+ mouse.x + " Y: " +  mouse.y;
        ctx.fillText(str , 10 ,18);
        var str = "Mouse world X: "+ mouseWorldPos.x.toFixed(2) + " Y: " +  mouseWorldPos.y.toFixed(2);
        ctx.fillText(str , 10 ,36);
        
        
        // if not over request a new animtion frame
        if(!endItAll){
           requestAnimationFrame(update);
        }else{
            // if done remove the canvas
            var can = document.getElementById("canv");
            if(can !== null){
                document.body.removeChild(can);
            }       
            // flag that we are ready to start again