With the use of bivariate wavelets, the applications of wavelets to surface subdivision methods becomes much more powerful than the use of biorthogonal wavelets. This book illustrates how symmetry can be used to improve surface visual quality and how the matrix-valued surface subdivision stencils that are included allow for the prediction of tangent planes and unit surface from the coarse control net. The text offers an up-to-date rigorous treatment of wavelet and frame-based surface multi-resolution theory, algorithms, and methods, together with matrix-valued and conventional surface subdivision schemes, integrated in a unified wavelet subdivision mathematics toolbox.