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The Present paper deals with a special type of interpolation problem, in which we have prescribed the values of the function at Ki and Ki+1 and the whole interval is divided into n equal sub-intervals of width.. We will derive a spline function of Degree 3 which will be able to interpolate this polynomial function, we name it three point spline (TPS). We have shown here how to change the next control point during further interpolation. We have also discussed the case, of whether this spline can be used for evaluating curvature.