Implicitization and parametrization of quadratic surfaces with one simple base point
Implicitization and parametrization of quadratic surfaces with one simple base point
复制标题
DOI：
10.1145/1390768.1390776
复制
发表时间：
2008-07
期刊：
影响因子：
--
通讯作者：
Xuhui Wang;Falai Chen;J. Deng
中科院分区：
文献类型：
--
作者：
Xuhui Wang;Falai Chen;J. Deng
讨论了单基点二次曲面的隐式化和参数化问题。实现隐式形式与参数形式转换的关键是计算三个线性无关的运动平面，我们称之为二次曲面的弱u基。从参数形式开始计算弱u基，然后求出其隐式方程。从弱u基中也可以很容易地得到反演公式。基于一个基点的二次曲面上存在一条自交线的观察，提出了一种由隐式形式转化为参数形式的方法。计算自交线后，我们可以得到弱u基，由此可以很容易地得到参数方程。给出了一种计算单基点二次曲面自交线的方法。
This paper discusses implicitization and parametrization of quadratic surfaces with one simple base point. The key point to fulfill the conversion between the implicit and the parametric form is to compute three linearly independent moving planes which we call the weak u-basis of the quadratic surface. Beginning with the parametric form, it is easy to compute the weak u-basis, and then to find its implicit equation. Inversion formulas can also be obtained easily from the weak u-basis. For conversion from the implicit into the parametric form, we present a method based on the observation that there exists one self-intersection line on a quadratic surface with one base point. After computing the self-intersection line, we are able to derive the weak u-basis, from which the parametric equation can be easily obtained. A method is also presented to compute the self-intersection line of a quadratic surface with one base point.