我的旋转矩阵有什么问题？

Question

//---------------------------------------------------------------------------
//  arbitraryRotate - rotates v theta degrees around n
//---------------------------------------------------------------------------
private static Vector3D arbitraryRotate(Vector3D v, Vector3D n, double theta)
{
    theta = Math.toRadians(theta);
    double cosTheta = Math.cos(theta);
    double sinTheta = Math.sin(theta);

    double M11 = n.x * n.x * (1 - cosTheta) + cosTheta;
    double M12 = n.x * n.y * (1 - cosTheta) + (n.z * sinTheta);
    double M13 = n.x * n.z * (1 - cosTheta) - (n.y * sinTheta);

    double M21 = n.x * n.y * (1 - cosTheta) - (n.z * sinTheta);
    double M22 = n.y * n.y * (1 - cosTheta) + cosTheta;
    double M23 = n.y * n.z * (1 - cosTheta) + (n.x * sinTheta);

    double M31 = n.x * n.z * (1 - cosTheta) + (n.y * sinTheta);
    double M32 = n.y * n.z * (1 - cosTheta) - (n.x * sinTheta);
    double M33 = n.z * n.z * (1 - cosTheta) + cosTheta;

    return new Vector3D(v.x * M11 + v.y * M21 + v.z * M31,
                        v.x * M12 + v.y * M22 + v.z * M32,
                        v.x * M13 + v.y * M23 + v.z * M33);
}

Could anyone tell me what is wrong with my matrix please? Rotation around the Z-Axis works perfectly however X and Y axis rotations result in distortions.

Answer 1

Your matrix is set up improperly. Here is how you rotate properly

1. Create a rotation matrix that rotates your axis to lie along the XZ plane
2. Create a rotation matrix that rotates that new axis to lie along the Z axis
3. Use the Z-axis rotation matrix to rotate by theta degrees about the Z axis.
4. Multiply by the inverse of 2
5. Multiply by the inverse of 1.

You get

new vector = (Rx^-1)(Ry^-1)RzRyRx(original vector)

Here's a link that spells it out well. You don't have to extend your vectors and matrices to 4 dimensions - that's only for the purpose of translation if you're rotating about an arbitrary line in space, not a vector stemming from the origin.