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

问题

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?

回答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.

回答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();

回答3:

Maybe helpful:

Live demo of how to find actual coordinates of transformed points

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]})`);

来源：https://stackoverflow.com/questions/15133977/how-to-calculate-svg-transform-matrix-from-rotate-translate-scale-values

标签

svg

coordinate-transformation