We demonstrate how algorithms to compute hierarchical triangular meshes. We can generate the hierarchical triangular meshes using level-of-detail for the mesh data structure. We perform hierarchical regional partitions using Ward's method with hierarchical data structure to achieve the level-of-detail. The meshes using this data structure can be hierarchically compressed and be unpacked at a faster pace. Additionally, we introduce the adaptive mesh generation algorithms for the parameters of computational mechanics by setting some kind of metrics in the level-of-detail.