@InCollection{weinkauf12b,
  author    = {T.~Weinkauf and H.~Theisel and O.~Sorkine},
  title     = {Cusps of Characteristic Curves and Intersection-Aware Visualization of Path and Streak Lines},
  booktitle = {Topological Methods in Data Analysis and Visualization II},
  publisher = {Springer},
  year      = {2012},
  editor    = {R.~Peikert and H.~Hauser and H.~Carr and R.~Fuchs},
  series    = {Mathematics and Visualization},
  pages     = {161--176},
  abstract  = {We analyze characteristic curves of vector fields and report on locations
              where they have cusps in their spatial projection, i.e., isolated
              points on the curve with abruptly turning tangent direction. Cusps
              appear in places where a projection of the corresponding tangent
              curve vector field exhibits critical points. We show that such cusps
              are only possible for streak and path lines, whereas they cannot
              appear on stream and time lines. Cusps turn out to be closely related
              to self-intersections of characteristic curves. We utilize this information
              in a new algorithm to create uncluttered static visualizations of
              path and streak lines.},
  url = {http://tinoweinkauf.net/publications/absweinkauf12b.html},
}