Point and derivates over sphere

Vector3 EvaluateOnSphere(float r, float theta, float psi, float offsetTheta, float offsetPsi){

    Vector3 v = new Vector3(
        Mathf.Cos(2f*Mathf.PI*theta+offsetTheta)*Mathf.Sin(2f*Mathf.PI*psi+offsetPsi),
        Mathf.Cos(2f*Mathf.PI*psi+offsetPsi),
        Mathf.Sin(2f*Mathf.PI*theta+offsetTheta)*Mathf.Sin(2f*Mathf.PI*psi+offsetPsi)
    );

    return r * v;

}

Vector3 EvaluateDerivateSphere(float theta, float psi, float magTheta, float magPsi, float offsetTheta, float offsetPsi){

    Vector3 vtheta = new Vector3 (
        -Mathf.Sin (2f * Mathf.PI * theta + offsetTheta) * Mathf.Sin (2f * Mathf.PI * psi + offsetPsi),
        0f,
        Mathf.Cos (2f * Mathf.PI * theta + offsetTheta) * Mathf.Sin (2f * Mathf.PI * psi + offsetPsi)
        );

    vtheta.Normalize ();

    Vector3 vpsi = new Vector3 (
        Mathf.Cos (2f * Mathf.PI * theta + offsetTheta) * Mathf.Cos (2f * Mathf.PI * psi + offsetPsi),
        -Mathf.Sin (2f * Mathf.PI * psi + offsetPsi),
        Mathf.Sin (2f * Mathf.PI * theta + offsetTheta) * Mathf.Cos (2f * Mathf.PI * psi + offsetPsi)
    );

    vpsi.Normalize ();

    return magTheta * vtheta + magPsi * vpsi;

}