Abstract: A technique for compression and expansion of a function defined upon an M-dimensional manifold embedded in N-dimensional space uses a second generation wavelet transform and a modified zerotree bit-encoding scheme. Typically, a function is defined upon a two-dimensional manifold embedded in three-dimensional space, such as a sphere. A geometric base is chosen as a coarse initial model of the manifold. Second generation wavelets for the function are calculated using a triangular subdivision scheme in order to subdivide the geometric base in order to produce a refined triangular mesh. The wavelet coefficients are defined at the vertices of the triangles in the triangular mesh. A tree structure is created in which each node of the tree structure represents an associated triangle of the triangular mesh. Each triangle in the mesh is recursively subdivided into four subtriangles and each associated node in the tree structure also has four children, which correspond to the four subtriangles.