Interpolatory subdivision scheme for geometric volumetric modeling

In this paper, we propose a tensor product interpolatoty volumetric subdivision scheme based on the 4-point curve subdivision scheme over the hexahedron lattice and analyze its convergence and smooth conditions using the associated generate function. The concept of volume on volume is introduced to compute and visualize the temperature field using the tensor product volumetric subdivision scheme. The limit of this sequence is a continuous geometric solid that interpolates the initial vertices of the lattice and given temperature values.