We present a readily accessible web-based interactive system for ray casting-based flow visualization in quotient spaces and ${\mathbb{S}^3}$. It is the result of a long-term close collaboration with researchers from symplectic geometry, and focuses on accessibility, flexibility, and provenance. By storing its state in URLs and providing a version-aware mechanism to link from images in PDFs to the online tool in the state that produced the image, we ensure reproducibility, explorability, and collaboration. We exemplify the utility of our approach with examples from mathematics and symplectic geometry.

This paper extends the concept and the visualization of vector field topology to vector fields with discontinuities. We address the non-uniqueness of flow in such fields by introduction of a time-reversible concept of equivalence. This concept generalizes streamlines to streamsets and thus vector field topology to discontinuous vector fields in terms of invariant streamsets. We identify respective novel critical structures as well as their manifolds, investigate their interplay with traditional vector field topology, and detail the application and interpretation of our approach using specifically designed synthetic cases and a simulated case from physics.