论文标题
计算机辅助设计中理性和NURB的可开发表面的表征
Characterisation of rational and NURBS developable surfaces in Computer Aided Design
论文作者
论文摘要
在本文中，我们根据边界曲线的开花和三个理性功能$λ$，$ m $，$ν$提供了理性开发表面的表征。在此框架中，修订了可开发表面的属性。特别是，通过函数$λ$，$ m $，$ν$获得了一个封闭的代数公式，以获得表面回归的边缘，该功能与在标准分解中出现的范围曲线之一的参数衍生物中出现的标准分解与裁决及其派生的导演曲线的参数相关。还表明，所有合理的开发表面都可以描述为一组可开发的表面，可以用常数的$λ$，$ m $，$ν$构建。结果很容易扩展到有理样条的可开发表面。
In this paper we provide a characterisation of rational developable surfaces in terms of the blossoms of the bounding curves and three rational functions $Λ$, $M$, $ν$. 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 $Λ$, $M$, $ν$, 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 $Λ$, $M$, $ν$ . The results are readily extended to rational spline developable surfaces.
