Numerical computation of isolated points for implicit curves and surfaces

Current algorithms for implicit curves and stufaces usually miss isolated points. This paper proposes a numerical solution for this problem, assuming that we are sampling a curve (resp., a surface) by means of some kind of space decomposition (e.g. bintree, quadtree, octree, etc.) of an axis-aligned bounding box into smaller cells. The idea is to find an isolated point of an implicit curve (resp., an implicit surface) inside a small 2D square cell (resp. a small 3D box cell).