Vectorizing vortex-core lines is crucial for high-quality visualization and analysis of turbulence. While several techniques exist in the literature, they can only be applied to classical fluids. As quantum fluids with turbulence are gaining attention in physics, extracting and visualizing vortex-core lines for quantum fluids is increasingly desirable. In this article, we develop an efficient vortex-core line vectorization method for quantum fluids enabling real-time visualization of high-resolution quantum turbulence structure. From a dataset obtained through simulation, our technique first identifies vortex nodes based on the circulation field. To vectorize the vortex-core lines interpolating these vortex nodes, we propose a novel graph-based data structure, with iterative graph reduction and density-guided local optimization, to locate sub-grid-scale vortex-core line samples more precisely, which are then vectorized by continuous curves. This vortex-core representation naturally captures complex topology, such as branching during reconnection. Our vectorization approach reduces memory consumption by orders of magnitude, enabling real-time visualization performance. Different types of interactive visualizations are demonstrated to show the effectiveness of our technique, which could help further research on quantum turbulence.

Superfluidity is a special state of matter exhibiting macroscopic quantum phenomena and acting like a fluid with zero viscosity. In such a state, superfluid vortices exist as phase singularities of the model equation with unique distributions. This paper presents novel techniques to aid the visual understanding of superfluid vortices based on the state-of-the-art non-linear Klein-Gordon equation, which evolves a complex scalar field, giving rise to special vortex lattice/ring structures with dynamic vortex formation, reconnection, and Kelvin waves, etc. By formulating a numerical model with theoretical physicists in superfluid research, we obtain high-quality superfluid flow data sets without noise-like waves, suitable for vortex visualization. By further exploring superfluid vortex properties, we develop a new vortex identification and visualization method: a novel mechanism with velocity circulation to overcome phase singularity and an orthogonal-plane strategy to avoid ambiguity. Hence, our visualizations can help reveal various superfluid vortex structures and enable domain experts for related visual analysis, such as the steady vortex lattice/ring structures, dynamic vortex string interactions with reconnections and energy radiations, where the famous Kelvin waves and decaying vortex tangle were clearly observed. These visualizations have assisted physicists to verify the superfluid model, and further explore its dynamic behavior more intuitively.