In every computer graphics oriented application today, it is a common practice to texture 3D models as a way to obtain realistic material. As part of this process, mesh texturing, deformation, and visualization are all key parts of the computer graphics field. This PhD dissertation was completed in the context of these three important and related fields in computer graphics. The article presents techniques that improve on existing state-of-the-art approaches related to continuity and interpolation in texture space (texturing), object space (deformation), and screen space (rendering).