Gradient-Preserving Cuts for Scalar Representations of Vector Fields

我们提出了一种方法来表示矢量场（通常是从流模拟或流测量方法）作为（共）梯度的标量场。由于它是已知的，在一般情况下，这是不可能的光滑标量场，我们介绍了标量场的梯度保持削减的概念。我们给出了它的精确定义并研究了它的性质。这样，矢量场可以精确地表示为标量场的（协）梯度（2D），或者表示为两个标量场梯度的叉积（3D）。我们探讨是否在此基础上，我们可以建立一个替代的方法，流水线集成比传统的集成技术更快，更准确。如果成功的话，这将影响流场可视化中的许多标准方法。我们的目标是通过引入新的基于纹理的流可视化技术和新的方法来证明这一点，用于精确的Clebsch图计算3D无发散流。

We propose an approach to represent vector fields (usually resulting from flow simulation or flow measurement approaches) as the (co-)gradient of a scalar field. Since it is known that in general this is impossible for smooth scalar fields, we introduce the concept of gradient-preserving cuts in scalar fields. We give an exact definition and study its properties. With this, vector fields can be exactly represented as (co-)gradients of scalar fields (2D), or as cross product of two scalar field gradients (3D). We explore whether based on this we can establish an alternative approach to stream line integration being both faster and more accurate than traditional integration techniques. If successful, this influences a number of standard approaches in Flow Visualization. We aim in demonstrating this by introducing new texture based Flow Visualization techniques and new methods for exact Clebsch map computation for 3D divergence-free flows.