In this thesis we present a fast, table-driven isosurface extraction technique on volumetric data. Unlike Marching Cubes or other cell-based algorithms, the proposed polygonization generates convex negative space inside individual cells, enabling fast collision detection on the triangulated isosurface. In our implementation, we are able to perform over 2 million point classifications per second. The algorithm is driven by an automatically constructed look-up table that stores compact decision trees by sign configurations. The decision trees determine triangulations dynamically by values at cell corners. Using the same technique, we can perform fast, crack-free multi-resolution contouring on nested grids of volumetric data. The method can also be extended to extract isosurfaces on arbitrary convex, space-filling polyhedra.