Visualization of Integral Curves in Plane Fields

This thesis explores methods to visualise contact geometries, which are interpreted as plane field, by using curves related to properties like curvature and torsion, as well as using vector field properties like the eigenvectors of the Jacobian matrix. First we introduce some mathematical fundamentals of differential geometry which are needed to understand and construct the curves introduced. As there are a lot of concepts on curves and vector field analysis, we give a short overview on already explored concepts like tensor field lines and geodesics as well as over-twisted discs. Based on these, we introduce our methods to construct novel curves with the above mentioned properties on multiple vector fields, as well as surfaces which are spanned by a multiple number of these curves on the same field. We analyse our results on a multiple number of different plane fields ranging from simple source/sink fields, over overtwisted discs to a vector field describing convective flow in a closed container. Lastly, we discuss the extension of the presented methods and possible further research.