ON GENERATING TOPOLOGICALLY CONSISTENT ISOSURFACES FROM UNIFORM SAMPLES

A set of sample points of a function of three variables may be visualized by defining an interpolating function f of the samples and examining isosurfaces of the form f(x, y, z) = t for various values of t. To display the isosurfaces on a graphics device, it is desirable to approximate them with piecewise triangular surfaces that (a) are geometrically good approximations, (b) are topologically consistent, and (c) consist of a small number of triangles. By topologically consistent we mean that the topology of the piecewise triangular surface matches that of the surface f(x, y, z) = t, i.e., the interpolant f determines both the geometry and the topology of the piecewise triangular surface. In this paper we provide an efficient algorithm for the case in which f is the piecewise trilinear interpolant; for this case, existing methods fail to satisfy all three of the above conditions simultaneously.