Subdivision for curves and surfaces has gained popularity in Computer Graphics and Computer Aided Geometric Design during the past two decades. In this dissertation, we design a hexahedral-based, approximation scheme. Ternary wavelets based on an interpolating 4-point ternary stationary subdivision scheme for compressing fractal-like signals are introduced. In this dissertation, error bounds between binary/ternary subdivision curves/surfaces and their control polygons after k-fold subdivision in terms of the maximal differences of the initial control point sequences and constants that depend...