Abstract
A \(C^1\) rational quadratic trigonometric interpolating function with three parameters is developed. The order of approximation of the developed \(C^1\) trigonometric interpolant is \(O( {h_i^2 })\). The \(C^1\) rational quadratic trigonometric function is extended to a \(C^1\) bivariate rational quadratic trigonometric function. The developed \(C^1\) bivariate trigonometric interpolant has six parameters in each rectangular patch. Automatic selection schemes for parameters are developed to preserve the positive shape of curve and surface data using \(C^1\) rational quadratic trigonometric function and \(C^1\) bivariate rational quadratic trigonometric function respectively. Performing the result, it is noticed that developed positivity preserving interpolation schemes are fast, efficient and well suited for all data types. Several numerical examples are presented to ascertain the correctness and usability of developed schemes.
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