Approximating normals for marching cubes applied to locally supported isosurfaces

We present some new methods for computing estimates of normal vectors at the vertices of a triangular mesh surface approximation to an isosurface which has been computed by the marching cube algorithm. These estimates are required for the smooth rendering of triangular mesh surfaces. The conventional method of computing estimates based upon divided difference approximations of the gradient can lead to poor estimates in some applications. This is particularly true for isosurfaces obtained from a field function, which is defined only for values near to the isosurface. We describe some efficient methods for computing the topology of the triangular mesh surface, which is used for obtaining local estimates of the normals. In addition, a new, one pass, approach for these types of applications is described and compared to existing methods.