Drew - 1 year ago 175
Javascript Question

# Find the Rotation and Skew of a Matrix transformation

I have the the following Transform Matrix in CSS

``````// rotate the element 60deg
element.style.transform = "matrix(0.5,0.866025,-0.866025,0.5,0,0)"
``````

And i can find the rotation using this...

``````// where a = [0.710138,0.502055,-0.57735,1,0,0]
var rotation = ((180/Math.PI) * Math.atan2( ((0*a[2])+(1*a[3])),((0*a[0])-(1*a[1]))) - 90
console.log(rotation); // ~60
``````

Similarly for skew if...

``````// skew(30deg,-50deg)
element.style.transform = "matrix(1,-1.19175,0.57735,1,0,0)"

var skewY = ((180/Math.PI) * Math.atan2( ((0*a[2])+(1*a[3])),((0*a[0])-(1*a[1]))) - 90;
var skewX = (180/Math.PI) * Math.atan2( ((1*a[2])+(0*a[3])),((1*a[0])-(0*a[1])));

console.log([skewX,skewY]); // ~= [30,-50]
``````

However as soon as i use both skew and rotation everything goes weird not least because the formula for rotation is identical to that of skew... so the formulas can't be right.

How do i determine both rotation & skew where both attributes have been applied and all i know is the Matrix Transform.

Also scale messed up my skew values, which i dont think it should.

i needed same functionality and today i ended up with this code that works very good.

i took inspiration from here: https://www.youtube.com/watch?v=51MRHjKSbtk and from the upper answer, without the hint QR decomposition i would never find it out

I worked on a 2x2 case, i will try to expand to 2x3 to include also translations. But it should be easy

``````var a = [a, c, b, d, e, f];
var qrDecompone = function(a) {
var angle = Math.atan2(a[1], a[0]),
denom = Math.pow(a[0], 2) + Math.pow(a[1], 2),
scaleX = Math.sqrt(denom),
scaleY = (a[0] * a[3] - a[2] * a[1]) / scaleX,
skewX = Math.atan2(a[0] * a[2] + a[1] * a[3], denom);
return {
angle: angle / (Math.PI / 180),  // this is rotation angle in degrees
scaleX: scaleX,                  // scaleX factor
scaleY: scaleY,                  // scaleY factor
skewX: skewX / (Math.PI / 180),  // skewX angle degrees
skewY: 0,                        // skewY angle degrees
translateX: a[4],                // translation point  x
translateY: a[5]                 // translation point  y
};
};
``````

It looks like that the last two items in the transformMatrix, before decomposition, are translation values. You can extract them directly.

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