Rendering and Extracting Extremal Features in 3D Fields

Visualizing and extracting three‐dimensional features is important for many computational science applications, each with their own feature definitions and data types. While some are simple to state and implement (e.g. isosurfaces), others require more complicated mathematics (e.g. multiple derivatives, curvature, eigenvectors, etc.). Correctly implementing mathematical definitions is difficult, so experimenting with new features requires substantial investments. Furthermore, traditional interpolants rarely support the necessary derivatives, and approximations can reduce numerical stability. Our new approach directly translates mathematical notation into practical visualization and feature extraction, with minimal mental and implementation overhead. Using a mathematically expressive domain‐specific language, Diderot, we compute direct volume renderings and particle‐based feature samplings for a range of mathematical features. Non‐expert users can experiment with feature definitions without any exposure to meshes, interpolants, derivative computation, etc. We demonstrate high‐quality results on notoriously difficult features, such as ridges and vortex cores, using working code simple enough to be presented in its entirety.