Feature tracking algorithms usually rely on operators for identifying regions of interest. One of these commonly used
operators is to identify parallel vectors introduced by Peikert and Roth.<sup>4</sup> In this paper, we propose a new and improved
method for finding parallel vectors in 3D vector fields. Our method uses a two-stage approach where in the first stage we extract solution points from 2D faces using Newton-Raphson method, and in the second stage, we use analytical tangents to trace solution lines. The distinct advantage of our method over the previous method lies in the fact that our algorithm does not require a very fine grid to find all the important topological features. As a consequence, the extraction phase does not have to be at the same resolution as the original dataset. More importantly, the feature lines extracted are topologically consistent. We demonstrate the tracing algorithm with results from several datasets.