Circle double-expanding-dichotomy algorithm for numerical calculation of distance from point to implicit curve

Abstract

The invention provides a circle double-expanding-dichotomy algorithm for the numerical calculation of a distance from a point to an implicit curve and has the advantages of high precision, high robustness, high algorithm efficiency and low demand on the smoothness of an implicit function; the method comprises the concrete steps of taking one point as the circle center, beginning from a circle with an allowable error as the radius, continuously doubly expanding the radius of the circle if the circle is not intersected with the hidden curve till one concentric circle is intersected with the hidden curve, then continuously dichotomising the radius of the concentric circle between the non-intersected inner circle and the intersected excircle to infinitely approach the inner circle to the excircle, and finally resolving the distance. An inferior arc evolutionary algorithm is adopted in the intersecting judging of the circle and the hidden curve, namely whether a function value and the circle center have the opposite signs is judged by performing reversed code operation on the dense equal diversion points of the circumference according to the sequence of the binary coding of the equal diversion points, if the function value and the circle center have the opposite signs, intersecting judgment is determined, otherwise, arcs in an inferior arc set are subjected to evolutionary processing such as deletion, shrinkage or splitting according to the functional value, the coverage range of the inferior arc set is reduced till the inferior arc is emptied and non-intersecting judgment is determined.

Description

technical field [0001] The invention relates to the field of numerical calculation, in particular to a numerical calculation method for providing a computer with the distance from a point to an implicit curve. Background technique [0002] The distance calculation method from point to implicit curve has important application value in the fields of pattern recognition, geometric modeling, computer vision, medical image processing, etc., and is also an important research basis for numerical analysis, computer science, reverse engineering and other disciplines. Since the analytical formula of the distance from the point to the implicit curve is generally difficult or even impossible to obtain, the calculation of the distance is usually a numerical calculation. [0003] Let the desired distance be the point p 0 The distance to the implicit curve f(x, y) = 0, the numerical calculation of the distance from the point to the implicit curve usually has a local method and a global me...

AI Technical Summary

Problems solved by technology

The global method can guarantee robust calculations, but the amount of calculations is large, and there are special requirements for implicit functions (such as convexity)

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