An affine transform for JavaScript. Saved for later.

affine.js

// an affine transformation matrix
class AffineTransform {
    // the matrix is represented as a 3x3 matrix
    // | A C Tx |
    // | B D Ty |
    // | 0 0 1  |

    // A, B, C, D are the coefficients of the linear transformation
    // Tx, Ty are the translation components
    constructor(A, C, Tx, B, D, Ty) {
        this.A = A;
        this.C = C;
        this.Tx = Tx;

        this.B = B;
        this.D = D;
        this.Ty = Ty;
    }

    mul(other) {
        const m = this;
        const n = other;

        const a = m.A*n.A + m.C*n.B;
        const c = m.A*n.C + m.C*n.D;
        const tx = m.A*n.Tx + m.C*n.Ty + m.Tx;

        const b = m.B*n.A + m.D*n.B;
        const d = m.B*n.C + m.D*n.D;
        const ty = m.B*n.Tx + m.D*n.Ty + m.Ty;

        this.A = a;
        this.C = c;
        this.Tx = tx;

        this.B = b;
        this.D = d;
        this.Ty = ty;
    }

    translate(tx, ty) {
        this.mul(Translation(tx, ty));
    }

    rotate(angle) {
        this.mul(Rotation(angle));
    }

    rotateDegrees(degrees) {
        this.mul(RotationDegrees(degrees));
    }

    scale(sx, sy) {
        this.mul(Scale(sx, sy));
    }

    shear(kx, ky) {
        this.mul(Shear(kx, ky));
    }
}

function Id() {
    return new AffineTransform(1, 0, 0, 0, 1, 0);
}

function Translation(tx, ty) {
    return new AffineTransform(1, 0, tx, 0, 1, ty);
}

function Rotation(angle) {
    const cos = Math.cos(angle);
    const sin = Math.sin(angle);
    return new AffineTransform(cos, -sin, 0, sin, cos, 0);
}

function RotationDegrees(degrees) {
    return Rotation(degrees * Math.PI / 180);
}

function Scale(sx, sy) {
    return new AffineTransform(sx, 0, 0, 0, sy, 0);
}

function Shear(kx, ky) {
    return new AffineTransform(1, kx, 0, ky, 1, 0);
}