C1-interpolation for vector field topology visualization

An application of C ¹ scalar interpolation for 2D vector field topology visualization is presented. Powell-Sabin and Nielson interpolants are considered which both make use of Nielson´s Minimum Norm Network for the precomputation of the derivatives in our implementation. A comparison of their results to the commonly used linear interpolant underlines their significant improvement of singularity location and topological skeleton depiction. Evaluation is based upon the processing of polynomial vector fields with known topology containing higher order singularities.