Subdivision Its Applications in Solid Modeling and Signal Compression

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 on the subdivision mask is estimated. The bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Our technique is independent of parameterizations therefore it can be easily and efficiently implemented.