Given an immersion f of a surface and a direction z in space, the height function , zf , in this direction is the projection of the immersed surface onto the directed line in the direction of z . For smooth surfaces, a Morse height function will have critical points where the tangent planes to the surface are perpendicular to the direction z , namely local minima, local maxima and saddles. Polyhedral surfaces will have critical points at the corresponding piecewise linear structures.
Height functions play an important role in describing tight immersions of surfaces in space.