Abstrakt
Given a polynomial space curve that has a rational rotation-minimizing frame (an RRMF curve), a methodology is developed to construct families of rational space curves with the same rotation-minimizing frame as at corresponding points. The construction employs the dual form of a rational space curve, interpreted as the edge of regression of the envelope of a family of osculating planes, having normals in the direction and distances from the origin specified in terms of a rational function as.
An explicit characterization of the rational curves generated by a given RRMF curve in this manner is developed, and the problem of matching initial and final points and frames is shown to impose only linear conditions on the coefficients of , obviating the non-linear equations (and existence questions) that arise in addressing this problem with the RRMF curve. Criteria for identifying low-degree instances of the curves are identified, by a cancellation of factors common to their numerators and denominators, and the methodology is illustrated by a number of computed examples.