二维和三维矢量场的可视化

矢量场可视化用来帮助人们直观理解二维和三维矢量场。由于目前的矢量场可视化方法只能展示二维矢量场的方向而不能展示强度，并且对于三维矢量场可视化的效果不太令人满意，因此本文提出了用线积分卷积来实现二维平面矢量场可视化，以及三维空间矢量场可视化的方法。对于线积分卷积中的流线跟踪，利用扩展的Bresenham画线算法的思想，实现了二维平面和三维空间流线的跟踪，并且通过建立一个二维表和三维表来分别存储二维平面矢量场和三维空间矢量场中每个点在流线中的上一个点和下一点的位置，来避免传统流线跟踪方法的冗余计算，提高了效率。对于二维平面矢量场，把线积分卷积的结果和矢量的强度进行加权平均，从而利用输出图像的纹理和颜色，共同来表现矢量场的方向和强度。对于三维空间矢量场，利用体线积分卷积（Volume Line Integral Convolution, Volume LIC）的方法来得到输出体纹理，并且用光线投射的体渲染方法来展示三维空间矢量场。结果显示出本文的方法能够清晰直观的看到二维平面矢量场和三维空间矢量场。

Visualization of 2D and 3D vector field

Vector field visualization can help people intuitively understand the two-dimensional and three-dimensional vector field. For two-dimensional vector field, the current methods of vector field visualization only provide the information about direction but not intensity. In addition, for the three-dimensional vector field, the vector field visualization result is not encouraging. This paper achieved two-dimensional and three-dimensional vector field visualization by the line integral convolution. In this paper we extend the idea of Bresenham line drawing algorithm to track the streamline on two-dimensional plane and in three-dimensional space. For each point either in the two-dimensional or the three-dimensional vector field our method will establish a two-dimensional or a three-dimensional table, respectively, to store the location of its previous and also next points along the streamline to remove the redundancy occurred from conventional streamline tracking methods. For the two-dimensional vector field, we applied the color transparency to the gray-scale LIC image and color coded motion amplitude image to enhance the motion strength on display. For the three-dimensional vector field, LIC was used to get the output texture pixels and the ray casting volume rendering method has been used to show the three-dimensional image. Simulation results show that patterns in the two-dimensional vector field and also in the three-dimensional vector field can be visualized clearly and intuitively.