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The C 1 rational cubic spline function (cubic/quadratic) with three parameters is used to construct a constrained interpolating curve that lies below or above an arbitrary straight line or between two straight lines. The data dependent sufficient conditions for the rational cubic interpolant bounded by two straight lines are derived on one parameter, while the other two are free parameters that will be useful for shape modification. Some numerical results will be presented by using Mathematicadoi:10.17576/jsm-2019-4803-23 fatcat:chbet7t5efaxdgl5shkatt77xe