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Interactive shape design is a fundamental tool in the areas of computer aided-design (CAD), computer aided manufacturing (CAM), computer aided design and drafting (CADD), computer-aided engineering (CAE) and computer-aided geometric design (CAGD). In this thesis, piecewise rational spline interpolants have been developed for the designing curves and surfaces where each curve segment of a piecewise spline interpolant is represented by two conic curve segments. Shape parameters used in the description of spline interpolants have been investigated. It has been demonstrated that the properties like convex hull, variation diminishing, global and local control of rational cubic and rational trigonometric cubic splines can be characterized by the rational quadratic and rational trigonometric quadratic splines. Practical examples have been used to identify that the techniques based on conic-like structures (rational quadratics) provide an extra degree of freedom for shape manipulation. It is noted that corresponding conic-like structures are computationally less expensive and achieve equivalently pleasing results as compare to rational and trigonometric cubic spline interplants. The method extends naturally to the design of surfaces.
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