Optimum Curve Matching Between Two Free-Form Curves for Modeling and Manufacturing

A new curve matching method is proposed to generate non-self-intersecting and non-twisted ruled surfaces for application in diverse fields such as heterogeneous object modeling, layered manufacturing, offsetting and multi-axis NC machining. The method establishes point-to-point correspondence represented by a set of ruling lines between two directrices of the ruled surface. The directrices are given as non-self-intersecting, closed, at least C¹ continuous, planar, B-spline curves. To match the points on the directrices, a heuristic optimization method developed with the objective is to maximize the sum of the inner products of the unit normals at the end points of the ruling lines and minimize the sum of the lengths of connecting ruling lines. The generated ruling lines can be used as cutter location data for multi-axis NC machining of ruled surfaces. Moreover, by subdividing the ruling lines into equal number of segments, one can construct a series of intermediate piecewise linear curves that represent the metamorphosis between the directrices. Implementation and examples are also presented.