# A Comprehensive Survey of Isocontouring Methods: Applications, Limitations and Perspectives
## 3 Tessellation-Based Algorithms
The method is used to extract the triangulated surface mesh and construct a volumetric mesh for all anatomical components within a sweep over all segmented CT slices. Since the volume of all components is meshed with a finite element mesh, it can be used directly for finite element calculations. In addition,  
Figure 6: Tessellation scheme for the marching tetrahedra algorithm based on the space-centered cubic lattice based on [28]. compared to the marching tetrahedra method, two further cases are considered during surface extraction within the tetrahedra and a seamless transition between anatomical components is ensured. The surface is then smoothed and simplified without losing the seamless transition. The method is used by the authors in bioluminescence tomography. In [33], [PERSON] presents a further extension of the classical marching tetrahedra method, the dual marching tetrahedra method. The method is a generalization of the cubelike method from cubes to tetrahedra and is used to render surfaces in a three-dimensional space. The dual marching tetrahedra method solves a fundamental problem in the original cuberille method, in which the separating surfaces are not necessarily manifolds. The method can be used for both structured and unstructured point clouds. [PERSON] et al. use the marching tetrahedra method to generate smooth surface meshes from multi-region medical images. For this purpose, the marching tetrahedra method is extended in [34] for use in multi-domain data, so that multi-region meshes are generated as a set of triangular surface pieces that consistently connect to each other at the material boundaries, combined with a method for the reconstruction of implicit surfaces. With this mesh generation strategy, it is possible to produce surface meshes using triangles from segmented medical data sets with multiple tissues. In addition, the terracing artifacts are avoided by the smooth description of the tissue boundaries before triangulation. [PERSON] et al. pursue a deep learning approach for high-resolution three-dimensional shape synthesis in [35], where the marching tetrahedra method is integrated into the deep learning framework. In the proposed approach, implicit and explicit surface representations are combined and the quality of shape synthesis is improved by the additional supervision defined directly on the extracted surface from the implicit field. Further research on the use of the marching tetrahedra method in the field of geological modeling can be found in [36; 37]. Another approach to determining isocontours in the field of tessellation-based algorithms comprises methods incorporating the triangulation of the point cloud to be analyzed. In [38], [PERSON] et al. present a fast isocontouring algorithm for scalar volume data. In a preprocessing step, seed cells are selected so that at least one cell per connected component of each isocontour is present. For the given isovalue, all cells of the previously defined seed cells that intersect the isocontour are then extracted. This leads to a significant reduction in calculation complexity. Another mesh-based method of approximating isocontours in a three-dimensional scalar field is the RoTri() function, introduced by [PERSON] et al. in [39]. A specific feature of the proposed algorithm is that unstructured three-dimensional point clouds can be processed. Furthermore, intersection points with an arbitrarily oriented plane can be determined. First, the unstructured three-dimensional point cloud is projected onto a two-dimensional plane so that the third component describing the variable under investigation is neglected for each point. The point cloud is then triangulated using Delaunay triangulation. Subsequently, each triangular vertex, i.e., each point from the point cloud, is again supplemented by the corresponding third component. This creates a three-dimensional, triangulated surface, as shown in Figure 7.  
Next, the method verifies whether there is an intersection point with the plane for each triangle generated in this way.