Subdivision based Interpolation with Shape Control

An interpolation technique with the capability of local shape control for meshes of arbitrary topology is presented. The interpolation is a progressive process which iteratively updates the given mesh, through a two-phase Doo-Sabin subdivision scheme, until a control mesh whose limit surface interpolates the given mesh is reached. For each iteration of the progression, the two-phase scheme works by first applying a modified Doo-Sabin subdivision to the input mesh and then applying the regular Doo-Sabin subdivision to the resulting mesh. The modified Doo-Sabin subdivision carries a parameter for each face of the input mesh. These parameters provide required freedom to adjust the interpolating subdivision surface at the user’s command. Local shape control is possible. It is proved that the progressive interpoaltion process converges for any parameters between 0 and 1. Therefore, this is a well-defined process. The progressive interpolation process satisfies both the local and global properties. Hence, the new technique can handle meshes of any size and is very faithful and efficient. Test cases that show the effectiveness of the new technique are included.