Many modern research areas face the challenge of meshing level sets of sampled scalar functions. While many algorithms focus on ensuring geometric qualities of the output mesh, recent attention has been paid to building topologically accurate Delaunay conforming meshes of any level set from such volumetric data. In this paper, we present an algorithm which constructs a surface mesh homeomorphic to the true level set of the sampled scalar function. The presented algorithm also produces a tetrahedral volumetric mesh of good quality, both interior and exterior to the level set. The meshing scheme presented substantially improves over the existing algorithms in terms of efficiency. Finally, we show that when the unknown sampled scalar function, for which the level set is to be meshed, is approximated by a specific class of interpolant, the algorithm can be simplified by taking into account the nature of the interpolation scheme so as to circumvent some of the critical computations which tend to produce numerical instability.