Transforming a plane with DirectXTK / DirectXMath

I have a 3D plane defined by three points and I want to transform it with a 4x4 matrix using DirectXTK.

I tried two ways to do this:

1. Transform the plane with Plane::Transform() method - this gives a very strange result.

2. Transform the three points and create a plane from the transformed points - this works fine.

I also tried to transpose the matrix before calling Plane::Transform() and it got the plane normal right, but the constant is wrong (plus that transposing the matrix really makes no sense to me).

void TestPlaneTransform()
{
    Vector3 p1(-2.4f, -2.0f, -0.2f);
    Vector3 p2(p1.x, p1.y + 1, p1.z);
    Vector3 p3(p1.x, p1.y, p1.z + 1);

    Plane plane(p1, p2, p3);
    Matrix m = Matrix::CreateTranslation(-4, -3, -2);

    // transform plane with matrix
    Plane result1 = Plane::Transform(plane, m);

    // transform plane with transposed matrix
    Plane result2 = Plane::Transform(plane, m.Transpose());

    // transform points with matrix
    Vector3 t1 = Vector3::Transform(p1, m);
    Vector3 t2 = Vector3::Transform(p2, m);
    Vector3 t3 = Vector3::Transform(p3, m);

    // plane from transformed points
    Plane result3(t1, t2, t3);

    result1.Normalize();
    result2.Normalize();
    result3.Normalize();
}

Here are the results after normalization:

result1 x:-0.704918027 y:-0.590163946 z:-0.393442601 w:0.196721300

result2 x:1.00000000 y:0.000000000 z:0.000000000 w:-1.59999990

result3 x:1.00000000 y:0.000000000 z:0.000000000 w:6.40000010

Plane::Transform() calls XMPlaneTransform which is part of the DirectXMath library and its documentation says simply "Transforms a plane by a given matrix.". I guess the method is just fine, but then what is wrong with my code?

Since you are calling Transform on the DirectXTK Plane it seems that it's not required to have it normalized before doing the call. But the DirectXTK wiki for Plane::Transform states this:

Planes should be transformed by the inverse transpose of the matrix, which for pure rotations results in the same matrix as the original.

github.com/Microsoft/DirectXTK/wiki/Plane