三维无旋矢量场的一种新的可视化方法

A New Method to Visualize 3D Rotation-Free Vector Fields

提出了三维无旋矢量场的一种新的可视化方法,即构造空间曲面,使得矢量场在曲面上任意一点处垂直于该曲面。首先找到曲面所满足的偏微分方程组,通过采用类似于经典四阶龙格―库塔方法的数值解法对其求解,得到曲面上的离散点,然后进行三角剖分,从而得到逼近于曲面的空间三角网格。论文的偏微分方程组的求解借鉴了常微分方程求解算法的设计思想,构造出的曲面与传统的点图标和线图标相比,在更大程度上揭示了矢量场本身的连续性。

A new method to visualize 3D rotation-free vector fields is presented,which tries to construct a surface in space so that the vectors on it are all orthogonal to it.Firstly,the system of partial differential equations of the surface is established,and then solved by our numerical method similar to classical fourth order Runge-Kutta method.Finally,the discrete points corresponding to the numerical solutions are triangulated to approximate the desired surface.Our numerical method for the partial differential equations borrows the idea of solving ordinary differential equations and the surface constructed reveals the continuity of the vector fields to a greater degree than point icons and line icons.