In this work we propose a new method for a fast incremental voxelization of isosurfaces obtained by the trilinear interpolation of 3D data. Our objective consists in the fast generation of subvoxelized iso-surfaces extracted by a point-based technique similar to the Dividing Cubes algorithm. Our technique involves neither an exhaustive scan search process nor a graph-based search approach when generating iso-surface points. Instead an optimized incremental approach is adopted here for a rapid isosurface extraction. With a sufficient sampling subdivision criteria around critical points, the extracted isosurface is both correct and topologically consistent with respect to the piece-wise trilinear interpolant. Furthermore, the discretiza-tion scheme used in our method ensures obtaining thin-one voxel width-isosurfaces as compared to the given by the Dividing Cubes algorithm. The resultant sub-voxelized isosurfaces are efficiently tested against all possible configurations of the trilinear interpolant and real-world datasets.