How accurately the processed image represents the vector field depends on how accurately the line convolution kernels follow the flow fields stream lines. Since the convolution kernels are only discretely sampling a continuous flow field, they are inaccurate in general. Areas of flow that are changing slowly will be represented well, but rapidly changing regions of the flow field (such as the center of vortices and other singularities) will be incorrectly described or missed altogether.
There are various ways of optimizing the sampling intervals to minimize this this problem, with different tradeoffs between computation time and resulting accuracy. The numerical analysis topics involved are beyond the scope of this document, and are well covered elsewhere [16,64]. For our purposes, we'll use the simplest and least accurate method - a fixed spatial sampling interval.