CURVES GENERATED BY A 3-TERM DIFFERENCE ALGORITHM

Algorithms for the generation of curves and surfaces play a very impor tant role in shape design and modelling in CAD/CAM systems. In this pa per, a simple three term difference algorithm is studied in detail and it is concluded that this algorithm could generate both conic curves, general monomial curves, and exponential spiral curves which interpol ate the initial points. The geometric constructions of such curves and their properties are also obtained. Two shape control parameters are provided so that the shape of the generated curve can be adjusted acco rding to requirements. An immediate generalization of the method is th e generation of uniform surface data in R(d), d greater than or equal to 3.