The growth rate of the surface is controlled by the distance along the surface from the edge or some other specified growing zone. We then expand the length of edges based on a function of this distance. The distance along a surface is known as the geodesic distance, and unlike distance through normal space, it can't be computed directly from the positions of the vertices. To compute this, we use a technique from a paper called "Geodesics in Heat" by Crane, et al. It employs a novel method to compute geodesics using heat flow to calculate the gradient of the distance, rather than directly computing it through a Dijkstra-like search.