How to calculate SVG transform matrix from rotate/translate/scale values?

Question

I have following details with me :

<g transform="translate(20, 50) scale(1, 1) rotate(-30 10 25)">

Need to change above line to:

<g transform="matrix(?,?,?,?,?,?)">

Can anyone help me to achieve this?

Answer 1

Translate(tx, ty) can be written as the matrix:

1  0  tx
0  1  ty
0  0  1

Scale(sx, sy) can be written as the matrix:

sx  0  0
0  sy  0
0   0  1

Rotate(a) can be written as a matrix:

cos(a)  -sin(a)  0
sin(a)   cos(a)  0
0        0       1

Rotate(a, cx, cy) is the combination of a translation by (-cx, cy), a rotation of a degrees and a translation back to (cx, cy), which gives:

cos(a)  -sin(a)  -cx × cos(a) + cy × sin(a) + cx
sin(a)   cos(a)  -cx × sin(a) - cy × cos(a) + cy
0        0       1

If you just multiply this with the translation matrix you get:

cos(a)  -sin(a)  -cx × cos(a) + cy × sin(a) + cx + tx
sin(a)   cos(a)  -cx × sin(a) - cy × cos(a) + cy + ty
0        0       1

Which corresponds to the SVG transform matrix:

(cos(a), sin(a), -sin(a), cos(a), -cx × cos(a) + cy × sin(a) + cx + tx, -cx × sin(a) - cy × cos(a) + cy + ty).

In your case that is: matrix(0.866, -0.5 0.5 0.866 8.84 58.35).

If you include the scale (sx, sy) transform, the matrix is:

(sx × cos(a), sy × sin(a), -sx × sin(a), sy × cos(a), (-cx × cos(a) + cy × sin(a) + cx) × sx + tx, (-cx × sin(a) - cy × cos(a) + cy) × sy + ty)

Note that this assumes you are doing the transformations in the order you wrote them.

Answer 2

First get the g element using document.getElementById if it has an id attribute or some other appropriate method, then call consolidate e.g.

var g = document.getElementById("<whatever the id is>");
g.transform.baseVal.consolidate();

Answer 3

Maybe helpful:

1. Live demo of how to find actual coordinates of transformed points

2. An implementation of the accepted answer:

   function multiplyMatrices(matrixA, matrixB) {
       let aNumRows = matrixA.length;
       let aNumCols = matrixA[0].length;
       let bNumRows = matrixB.length;
       let bNumCols = matrixB[0].length;
       let newMatrix = new Array(aNumRows);
   
       for (let r = 0; r < aNumRows; ++r) {
           newMatrix[r] = new Array(bNumCols);
   
           for (let c = 0; c < bNumCols; ++c) {
               newMatrix[r][c] = 0;
   
               for (let i = 0; i < aNumCols; ++i) {
                   newMatrix[r][c] += matrixA[r][i] * matrixB[i][c];
               }
           }
       }
   
       return newMatrix;
   }
   
   let translation = {
       x: 200,
       y: 50
   };
   let scaling = {
       x: 1.5,
       y: 1.5
   };
   let angleInDegrees = 25;
   let angleInRadians = angleInDegrees * (Math.PI / 180);
   let translationMatrix = [
       [1, 0, translation.x],
       [0, 1, translation.y],
       [0, 0, 1],
   ];
   let scalingMatrix = [
       [scaling.x, 0, 0],
       [0, scaling.y, 0],
       [0, 0, 1],
   ];
   let rotationMatrix = [
       [Math.cos(angleInRadians), -Math.sin(angleInRadians), 0],
       [Math.sin(angleInRadians), Math.cos(angleInRadians), 0],
       [0, 0, 1],
   ];
   let transformMatrix = multiplyMatrices(multiplyMatrices(translationMatrix, scalingMatrix), rotationMatrix);
   
   console.log(`matrix(${transformMatrix[0][0]}, ${transformMatrix[1][0]}, ${transformMatrix[0][1]}, ${transformMatrix[1][1]}, ${transformMatrix[0][2]}, ${transformMatrix[1][2]})`);