In the first part of the paper a planar generalization of offset curves is introduced and some properties are derived. In particular, it is seen that these curves exhibit good regularity properties and a study on self-intersection avoidance is performed. The representation of a rational curve as the envelope of its tangent lines, following the approach of Pottmann, is revisited to give the explicit expression of all rational generalized offsets. Other famous shapes, such as constant width curves, bicycle tire-tracks curves and Zindler curves are related to these generalized offsets. This gives rise to the second part of the paper, where the particular case of rational parameterizations by a support function is considered and explicit families of rational constant width curves, rational bicycle tire-track curves and rational Zindler curves are generated and some examples are shown.

在本文的第一部分中，介绍了偏移曲线的平面推广，并推导出了一些性质。特别是，可以看出这些曲线表现出良好的规律性，并且对自相交避免进行了研究。有理曲线表示为它的包络线在 Pottmann 的方法之后，切线被重新访问以给出所有有理广义偏移的明确表达。其他著名的形状，例如等宽曲线、自行车轮胎痕迹曲线和 Zindler 曲线都与这些广义偏移有关。这就产生了论文的第二部分，其中考虑了支持函数有理参数化的特殊情况，并生成了有理等宽曲线、有理自行车轮胎轨道曲线和有理 Zindler 曲线的显式族，并给出了一些例子.