Characterizations of the set of rational parametric curves with rational offsets.

*(English)* Zbl 0813.65032
Laurent, Pierre-Jean (ed.) et al., Curves and surfaces in geometric design. Papers from the 2nd international conference on curves and surfaces, held in Chamonix-Mont-Blanc, France, June 10-16, 1993. Wellesley, MA: A K Peters. 153-160 (1994).

Summary: Rational curves do not generally have rational offsets. We give an analytic characterization of rational curves with rational offsets. We also propose a geometric characterization of these curves after showing that the set of rational curves with rational or piecewise rational arc length is equal to the set of caustics of the rational curves.

##### MSC:

65D17 | Computer aided design (modeling of curves and surfaces) |

41A20 | Approximation by rational functions |