This flashcard is just one of a free flashcard set. See all flashcards!

If we iterate the smoothing operator

until convergence, the will go to zero:

We know that approximates the Laplace of a function that interpolates the . Thus

The physical interpretation of is an area-minimizing membrane surface, comparable to the surface of a soap film suspended inside a wire loop.

By constraining higher-order derivatives of , we can model other surfaces such as a thin plate:

which gives

and produces a surface which minimizes curvature.