Positive interpolation by trigonometric functions

A (Formula presented.) rational quadratic trigonometric interpolating function with three parameters is developed. The order of approximation of the developed (Formula presented.) trigonometric interpolant is (Formula presented.). The (Formula presented.) rational quadratic trigonometric function is extended to a (Formula presented.) bivariate rational quadratic trigonometric function. The developed (Formula presented.) 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 (Formula presented.) rational quadratic trigonometric function and (Formula presented.) 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. © 2015, African Mathematical Union and Springer-Verlag Berlin Heidelberg.