Abstract 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.

Many algorithms for scientific visualization and image analysis are rooted in the world of continuous scalar, vector, and tensor fields, but are programmed in low-level languages and libraries that obscure their mathematical foundations. Diderot is a parallel domain-specific language that is designed to bridge this semantic gap by providing the programmer with a high-level, mathematical programming notation that allows direct expression of mathematical concepts in code. Furthermore, Diderot provides parallel performance that takes advantage of modern multicore processors and GPUs. The high-level notation allows a concise and natural expression of the algorithms and the parallelism allows efficient execution on real-world datasets.

Research scientists and medical professionals use imaging technology, such as computed tomography (CT) and magnetic resonance imaging (MRI) to measure a wide variety of biological and physical objects. The increasing sophistication of imaging technology creates demand for equally sophisticated computational techniques to analyze and visualize the image data. Analysis and visualization codes are often crafted for a specific experiment or set of images, thus imaging scientists need support for quickly developing codes that are reliable, robust, and efficient.