Curves generated by a three-term difference algorithm

Algorithms for the generation of curves and surfaces play a very important role in shape design and modelling in CAD/CAM systems. In this paper, 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 interpolate 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 according to requirements. An immediate generalization of the method is the generation of uniform surface data in Rd, d ≥ 3.