Make 2D Sprite Face Camera Using Vertex Shader - DirectX 9

Currently, I'm calculating the world matrix in C++ and then pass it to the shader to make the sprite always face the camera:

static D3DXVECTOR3 up(0, 0, 1);
D3DXMATRIX world, view, proj;

// get the world, view and projection matrix
g_pd3dDevice->GetTransform(D3DTS_WORLD, &world);
g_pd3dDevice->GetTransform(D3DTS_VIEW, &view);
g_pd3dDevice->GetTransform(D3DTS_PROJECTION, &proj);

D3DXMATRIX translation, invView, cameraPosition, rotation,invRotation;

// get the camera position by inversing the view matrix
D3DXMatrixInverse(&invView, NULL, &view);
cameraPosition = D3DXVECTOR3(invView._41, invView._42, invView._43);

// translate the sprite position to a world matrix
D3DXMatrixTranslation(&translation, spritePosition.x, spritePosition.y, spritePosition.z);

// calculate the world matrix rotation to look from
// the sprite position to the camera position
D3DXMatrixLookAtRH(&invRotation, &spritePosition, &cameraPosition, &up);
D3DXMatrixInverse(&rotation, NULL, &invRotation);

// pass the world * view * projection to the shader
world =  rotation * translation;
worldViewProj = matrix.rotation * matrix.view * matrix.proj;

g_pEffect->SetMatrix("WorldViewProj", &worldViewProj);

I've just been learning DirectX and HLSL for the past few days so I don't know if this is the optimal and correct way to do it. I thought it would have been better done in the vertex shader but I don't know how, please guide me.

SimpleMath in the DirectX Tool Kit includes Matrix::CreateBillboard and Matrix::CreateConstrainedBillboard which is specifically designed for creating this kind of transformation matrix.

inline Matrix Matrix::CreateBillboard(
    const Vector3& object,
    const Vector3& cameraPosition,
    const Vector3& cameraUp,
    const Vector3* cameraForward) noexcept
{
    using namespace DirectX;
    const XMVECTOR O = XMLoadFloat3(&object);
    const XMVECTOR C = XMLoadFloat3(&cameraPosition);
    XMVECTOR Z = XMVectorSubtract(O, C);

    const XMVECTOR N = XMVector3LengthSq(Z);
    if (XMVector3Less(N, g_XMEpsilon))
    {
        if (cameraForward)
        {
            const XMVECTOR F = XMLoadFloat3(cameraForward);
            Z = XMVectorNegate(F);
        }
        else
            Z = g_XMNegIdentityR2;
    }
    else
    {
        Z = XMVector3Normalize(Z);
    }

    const XMVECTOR up = XMLoadFloat3(&cameraUp);
    XMVECTOR X = XMVector3Cross(up, Z);
    X = XMVector3Normalize(X);

    const XMVECTOR Y = XMVector3Cross(Z, X);

    XMMATRIX M;
    M.r[0] = X;
    M.r[1] = Y;
    M.r[2] = Z;
    M.r[3] = XMVectorSetW(O, 1.f);

    Matrix R;
    XMStoreFloat4x4(&R, M);
    return R;
}

This is a port of the XNA Game Studio C# math library to C++ using DirectXMath.