A method of polygonizing an object calculates indicators that points within a set (Q) of points within three space representing the object likely lie near a surface discontinuity of the object. A global mesh is formed around a point that likely does not lie near a surface discontinuity (i.e. a reliable point). Local meshes are formed about reliable points on the frontier of this global mesh. Each local mesh is combined with the global mesh, thereby adding to the global mesh and advancing the frontier. Once a local mesh has been formed about each reliable point on the frontier and added to the global mesh, a local mesh may be formed about a point on the frontier that is more likely to lie near a surface discontinuity. The formation of local meshes can be repeated until no frontiers are left, or until all points have been added to the global mesh.