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We obtain the distribution of inflection points and singularities on a parametric rational cubic curve segment with aid of Mathematica (A System of for Doing Mathematics by Computer). The reciprocal numbers of the magnitudes of the end slopes determine the occurrence of inflection points and singularities on the segment. Its use enables us to check whether(More)
A method for family of G 2 Pythagorean hodograph (PH) quintic spiral transition from straight line to circle is discussed in this paper. This method is then extended to a pair of spirals between two straight lines or two circles. We derive a family of quintic transition spiral curves joining them. Due to flexibility and wide range of shape control(More)