Computing the minimum distance between a point and a NURBS curve
Computer-Aided Design
Computing the minimum distance between two Bézier curves
Journal of Computational and Applied Mathematics
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This paper presents an improved algebraic pruning method for point projection for Bézier curves. It first turns the point projection into a root finding problem, and provides a sim- ple but easily overlooked method to avoid finding invalid roots which is obviously irrelative to the closest point. The continued fraction method and its expansion are utilized to strengthen its robustness. Since NURBS curves can be eas- ily turned into Bézier form, the new method also works with NURBS curves. Examples are presented to illustrate the ef- ficiency and robustness of the new method. Keywords Point projection; NURBS curve; Continued fraction method; Algebraic pruning method