Authors: Tao Ju, Minxin Cheng, Xu Wang, Ye Duan
Abstract: Parallel vectors (PV), the loci where two vector fields are parallel, are commonly used to represent curvilinear features in 3D for data visualization. Methods for extracting PV usually operate on a 3D grid and start with detecting seed points on a cell face. We propose, to the best of our knowledge, the first provably correct test that determines the parity of the number of PV points on a cell face. The test only needs to sample along the face boundary and works for any choice of the two vector fields. A discretization of the test is described, validated, and compared with existing tests that are also based on boundary sampling. The test can guide PV-extraction algorithms to ensure closed curves wherever the input fields are continuous, which we exemplify in extracting ridges and valleys of scalar functions.