Flowspace: The Space Spanned by Pathlines, Timelines, Streaklines.

科学可视化--即将计算或测量的科学数据呈现给人类感官--是一个重要的研究领域。图片往往是最清晰、最快捷的方式，可以让科学家对实验或模拟有直观的感觉。遗憾的是，依赖时间的矢量场(如流体在所有点的速度)的可视化目前仅限于最初来自实验方法的几种基本技术。每一种技术都是条纹和时间线的变体，两者都是由粒子路径构建的。对为稳定流动开发的算法的粗略扩展最近补充了这些扩展。其中最值得注意的是流线的计算和显示，但这些只与稳态流体流动的物理相关。这个项目将把这些常用的技术放在一个一般的几何和数学框架内，并提出没有一个单一的方法最适合所有流动的概念。因此，它将研究一类更一般的算法，并将寻求将矢量场表示与所需的流动的时间相关特征(例如涡流、涡流或激波)的显示相匹配。为了探索这个参数空间，该项目将开发一套使用基于软件和硬件的技术的交互式矢量场可视化工具。这些方法将在典型的非定常矢量场上进行测试，即空间变量和时间变量中的线性和二次场。

Scientific visualization - that is, presenting computed or measured scientific data to human senses - is a vital area of research. Pictures are often the clearest and fastest way to give a scientist an intuitive feeling for an experiment or simulation. Unfortunately, visualization of time-dependent vector fields (such as velocity of a fluid at all points) is currently limited to a few basic techniques that originally came from experimental methods. Every technique is a variation on streaklines and timelines, both built from particle paths. Crude extensions to algorithms developed for steady flows have recently supplemented these. Most notable among these are the computation and display of streamlines, but these are only physically relevant for steady-state fluid flows.This project will place these commonly used techniques within a general geometric and mathematical framework, and advance the notion that no single method is best suited for all flows. Therefore, it will study a more general class of algorithms, and will seek to match a vector field representation to the display of a desired time-dependent feature of the flow (e.g. vortices, eddies, or shocks). To explore this parameter space, the project will develop a suite of interactive vector field visualization tools using both software- and hardware-based techniques. The methods will be tested on prototypical unsteady vector fields, namely linear and quadratic fields in the spatial and temporal variables.