Maintaining a moving mesh of a deforming surface is widely studied in various disciplines. However, difficulties arise with requirements of topology changes, homeomorphism between mesh and surface, and guarantees of triangle quality. This book proposes a mesh deformation algorithm to satisfy the above requirements. The general skin surface deformation framework is deployed to approximate objects and morph them freely in 3-dimension. This work completes the general skin deformation framework by introducing a new mesh point movement and scheduling function to overcome the previous difficulties.