In this paper we provide a characterisation of rational developable surfaces in terms of the blossoms of the bounding curves and three rational functions $\Lambda$, $M$, $\nu$. Properties of developable surfaces are revised in this framework. In particular, a closed algebraic formula for the edge of regression of the surface is obtained in terms of the functions $\Lambda$, $M$, $\nu$, which are closely related to the ones that appear in the standard decomposition of the derivative of the parametrisation of one of the bounding curves in terms of the director vector of the rulings and its derivative. It is also shown that all rational developable surfaces can be described as the set of developable surfaces which can be constructed with a constant $\Lambda$, $M$, $\nu$ . The results are readily extended to rational spline developable surfaces.

中文翻译：

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计算机辅助设计中合理和 NURBS 可展曲面的表征

在本文中，我们根据边界曲线的花朵和三个有理函数 $\Lambda$、$M$、$\nu$ 提供了有理可展曲面的表征。在此框架中修改了可展开曲面的属性。特别地，根据函数$\Lambda$、$M$、$\nu$得到了曲面回归边的封闭代数公式，这些函数与标准分解中出现的函数密切相关。根据规则的导向向量及其导数对其中一条边界曲线进行参数化的导数。还表明，所有有理可展曲面都可以描述为一组可展曲面，这些曲面可以用常数 $\Lambda$, $M$, $\nu$ 构造。结果很容易扩展到有理样条可展曲面。