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首页> 外文会议>International Conference on Computational Science - ICCA 2003 Pt.1 Jun 2-4, 2003 Melbourne, Australia and St. Petersburg, Russia >A New Differential Approach for Parametric-Implicit Surface Intersection
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A New Differential Approach for Parametric-Implicit Surface Intersection

机译：参数-隐式曲面相交的一种新的差分方法

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摘要

In this paper, we focus on the parametric-implicit surface intersection problem. In our approach, this problem is formulated in terms of an initial value problem of first-order ordinary differential equations (ODEs). To this end, we take advantage of the orthogonality at any point on the intersection curve between the tangent vector to that curve and the normal vector to the implicit surface. This yields an initial value system of ODEs that is numerically integrated through an adaptive Runge-Kutta method. In order to determine the initial value for this system, a simple procedure based on the scalar and vector fields associated with the function defining the implicit surface and its gradient is described. Such a procedure yields a starting point on the nearest branch of the intersection curve. The performance of the presented method is analyzed by means of some illustrative examples.
机译：在本文中，我们关注参数隐式曲面相交问题。在我们的方法中，此问题是根据一阶常微分方程（ODE）的初值问题来表述的。为此，我们利用与该曲线的切线向量和与隐式曲面的法线向量之间的相交曲线上任意点的正交性。这产生了ODE的初始值系统，该系统通过自适应Runge-Kutta方法进行了数值积分。为了确定该系统的初始值，描述了一种基于标量和矢量场的简单过程，该标量和矢量场与定义隐式表面及其梯度的函数相关联。这样的过程会在相交曲线的最近分支上产生一个起点。通过一些示例性实例分析了所提出方法的性能。

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