Subdivision Schemes and their Applications in Geometric Modeling

Subdivision is a basic tool to describe smooth curves and surfaces in computer aided geometric design. Since no single subdivision scheme can be adequate for every situation so, there is always a space to present new schemes. The main purpose of this dissertation is to introduce different kinds of subdivision schemes for curve and surface designing based on arity and complexity. Several explicit formulae for generation of mask of subdivision schemes are presented. Many well known existing schemes are special cases of our proposed schemes. Convergenceandsmoothnessofstationaryandnon-stationarysubdivisionschemesareevaluatedbyusingLaurentpolynomialmethodandasymptotic equivalence technique respectively. Some of remarkable properties of proposed subdivision schemes like Hölder regularity, support of basic limit function,errorbounds,totalabsolutecurvature,artifact,shrinkageeffect,limitstencil, convexity preservation, af?ne invariance and reproduction are discussed. The applications of the schemes developed have also been depicted through different example