Abstract
We present a new type of interpolating cubic-polynomial-curve connecting given two points with slopes given at these points. The curves are obtained by an extension of Ferguson's curves under a certain constraint. It is assured that the curves are contained within a given tolerance from the straight line connecting the two points. Conventional interpolating-curves cannot have this property. Further the curves are monotonic in the meaning of minimizing the number of inflection points, and having no singular points and no self-crossings. We show a mathematical framework to assure of this accuracy and monotony, and present an algorism to compute the curves.
