The slope preserving id positive modified quadratic shepard interpolant

We preserved positivity through a control over the minimum point to get a positive cubic Hermite (see Asim and Brodlie (3)) D. We think we are first to introduce this technique. Subsequently we extended the idea to preserve positivity by obtaining a control over the extremum point of the basis functions of the Modified Quadratic Shepard interpolant in ID. Since the version thus developed does not interpolate the given or estimated slopes, the need for a slope interpolating constrained Modified Quadratic Shepard interpolant was felt. In this paper, we constrain the Modified Quadratic Shepard interpolant to preserve positivity in one-dimensional interpolation such that the constrained interpolant also interpolates the slope data. We replace each basis function, by a positive spline which interpolates both the associated data point and slope at the data point while constraining the original curve to be positive. The extra knot in the spline provides the necessary flexibility which we avail for slope interpolation required. (author)