A robust parity test for extracting parallel vectors in 3D

Tao Ju, Minxin Cheng, Xu Wang, Ye Duan

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish
Article number06875965
Pages (from-to)2526-2534
Number of pages9
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number12
StatePublished - Dec 31 2014


  • Feature curve extraction
  • Parallel vectors
  • Parity test
  • Ridges and valleys


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