Comparison and Evaluation of Marching Cubes and Marching Tetrahedra

Isosurface extraction algorithms are widely applied in scalar volume data visualization and implicit surfaces rendering.The marching cubes and the marching tetrahedra are two classical isosurface extraction algorithms, which approximate the isosurfaces piecewise linearly via triangular mesh.The approximate errors result from two aspects.Firstly, the intersection point between the voxel's edge and the isosurface is approximately computed by linear interpolation.Secondly, the curved isosurface is approximated with piecewise linear triangular meshes.To evaluate the two isosurface extraction algorithms thoroughly, several algebraic surfaces with distinct shape features are adopted and tested in this paper.The detailed comparisons are made from the aspects of approximate accuracy, time and space complexities, etc.The evaluation results provide user a reference of selecting isosurface extraction algorithms.