Toward the uniform coverage of surfaces by scanning curves

This paper concerns the construction of curves for the coverage of surfaces. The question is how to produce a curve to cover a surface uniformly. The answer is of interest to a wide range of applications. Extended scanning curves which support both full scanning and sub-scanning of surfaces is proposed for enhancing the uniformity in surface coverage. A method for constructing such curves is presented. For a given parametric surface and a specified pitch, an extended scanning curve can be constructed to cover the surface such that the scan count of the curve varies according to the pitch count of the surface. The method has been illustrated and validated through curve construction for two surfaces. Resulting curves may give rise to regions of sub-scanning, depending on the given surface. It has also been demonstrated through quantitative analysis that extended scanning curves provide more uniform coverage of surfaces than those based on conventional scanning.