A hierarchical sampling approach for polygonizing variational implicit surfaces

This article discusses an enhanced polygonization algorithm for variational implicit surfaces. The polygonization scheme is a simple hierarchical adaptation of the Marching Cubes algorithm which takes advantage of some properties of variational implicits to produce a proper and efficient sampling of the surface. The technique exploits the fact that variational objects exhibit properties akin to Euclidean distance metrics, thus allowing the polygonizer to quickly ascertain that a given volume does not contain the surface. Timings show that this technique tends to perform faster than Bloomenthal's continuation polygonizer [Bloomenthal J. Graphics Gems IV 1994;324-49].