Approximate G1 continuous interpolation of a rectangular network of rational cubic curves

Abstract The problem of spanning a rectangular network of rational cubic curves with a smooth surface is discussed in this paper. Provided the network is compatible with a smooth surface, then algorithms for patch construction, optimization and subdivision are developed to construct an ‘approximately smooth’ surface, that is, G1 continuous to within some tolerance, composed of rational bicubic patches. The algorithms have been applied in the die and mould industry. The toolmaker constructs a wireframe model of an EDM (electro-discharge machining) electrode and the algorithms automatically construct the surface model. For toolmaking companies, this simplifies the surface modelling process making a highly-specialized and time-consuming task virtually automatic.

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