Analysis of the offset to a parabola
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Abstract Wei Lu has recently constructed a proper rational parameterization for the two-sided offset to a parabola—indicating that this locus, an irreducible curve of degree n = 6, is of genus 0. The theory of algebraic curves then requires that the parabola offset have 1 2 (n−1)(n−2) = 10 double points. One affine node and six affine cusps are readily identified by geometric arguments; we show that the remaining three double points are accounted for by a non-ordinary double point at infinity, having double points in its first and second neighborhoods.
[1] O. J. Peterson. The Double Points of Rational Curves , 1917 .
[2] Helmut Pottmann,et al. Rational curves and surfaces with rational offsets , 1995, Comput. Aided Geom. Des..
[3] Rida T. Farouki,et al. Analytic properties of plane offset curves , 1990, Comput. Aided Geom. Des..
[4] T. Sakkalis,et al. Pythagorean hodographs , 1990 .
[5] R. J. Walker. Algebraic curves , 1950 .