C1 rational quadratic trigonometric spline

A Bézier like C1 rational quadratic trigonometric polynomial spline is developed. It defines two shape parameters in each subinterval. The approximation and geometric properties are investigated. The curvature continuity is established. The developed rational quadratic trigonometric polynomial spline is extended to C1 piecewise rational bi-quadratic function with four shape parameters in each rectangular patch. Data dependent constraints are developed on the shape parameters in the description of piecewise rational quadratic and bi-quadratic trigonometric polynomial spline for shape preservation of curve and regular surface data. The developed shape preserving schemes provide tangent continuity in quadratic form and does not restrict interval length, derivatives or data.