Let P be a point on a smooth surface. The tangent plane at P is the plane through P that touches the surface. Equally, it is the plane containing all the tangent lines to smooth curves in the surface that pass through P. If r(u,v) is a parameterization of the surface about P = r(u0,v0), then the tangent plane is the plane through P parallel to ∂r/∂u(u0,v0) and ∂r/∂v(u0,v0). See tangent space.