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首页> 外文期刊>Computer-Aided Design >Parameterizing rational offset canal surfaces via rational contour curves
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Parameterizing rational offset canal surfaces via rational contour curves

机译：通过有理轮廓线对有理偏置渠面进行参数化

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摘要

A canal surface is the envelope of a 1-parameter set of spheres centered at the spine curve m(t) and with the radii described by the function r(t). Any canal surface given by rational m(t) and r(t) possesses a rational parameterization. However, an arbitrary rational canal surface does not have to fulfill the PN (Pythagorean normals) condition. Most (exact or approximate) parameterization methods are based on a construction of a rational unit normal vector field guaranteeing rational offsets. In this paper, we will study a condition which guarantees that a given canal surface has rational contour curves, which are later used for a straightforward computation of rational parameterizations of canal surfaces providing rational offsets. Using the contour curves in the parameterization algorithm brings another extra feature; the parameter lines do not unnecessarily wind around the canal surface. Our approach follows a construction of rational spatial MPH curves from the associated planar PH curves introduced in Kosinka and Lavicka (2010) [28] and gives it to the relation with the contour curves of canal surfaces given by their medial axis transforms. We also present simple methods for computing approximate PN parameterizations of given canal surfaces and rational offset blends between two canal surfaces.
机译：根管表面是1个参数集的球体的包络，球体的中心是脊柱曲线m（t），半径由函数r（t）描述。由有理m（t）和r（t）给出的任何运河表面都具有有理参数化。但是，任意有理渠表面不必满足PN（毕达哥拉斯法线）的条件。大多数（精确的或近似的）参数化方法都是基于保证有理偏移的有理单位法向矢量场的构造。在本文中，我们将研究一种条件，该条件可确保给定的运河表面具有合理的轮廓曲线，然后将其用于对提供合理偏移的运河表面的合理参数化进行直接计算。在参数化算法中使用轮廓曲线带来了另一个额外的功能。参数线不必绕管表面缠绕。我们的方法是根据Kosinka和Lavicka（2010）[28]中引入的相关平面PH曲线构造合理的空间MPH曲线，并将其与由中轴变换给出的运河表面轮廓曲线的关系。我们还提出了用于计算给定渠道面的近似PN参数化和两个渠道面之间的合理偏移混合的简单方法。

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