Error-Free Interpolation of Parametric Surfaces

Abstract

A Digital Differential analyzer (DDA) is a cost effective implementation for interpolating parametric curves and surfaces. However, the problems of register overflow and integer round-off have prevented it from being adopted by industry. Contrary to intuition, an increase in register capacity is shown to have no bearing on the register overflow problem. It is shown that there is a minimum number of interpolation steps K l below which register overflow occurs. Correspondingly, it is also shown that there exists a maximum number of interpolation steps K u above which the accumulation of integer round-off errors exceeds the acceptable limit. But, when K l >K u , conflict arises. A solution is given to resolve the possible conflict and to yield an error-free interpolation of curves and surfaces.