corespaceing3d

CoreSpacing3D is a research codebase for quantifying and interpreting projection bias in nearest-neighbour (NN) and minimum-spanning-tree (MST) spacings of dense cores and similar point distributions. The package is designed to bridge the gap between intrinsic three-dimensional structure and observationally accessible two-dimensional measurements, with a particular focus on applications in star-formation studies.

The code provides a flexible framework to generate synthetic 3D point distributions using a range of spherically symmetric and hierarchical models, including uniform, Gaussian, power-law, exponential, Plummer-like, shell, and Cartwright–Whitworth–style fractal distributions. These point sets can be rotated, projected into 2D, and optionally subjected to a simple beam-blending model to mimic the effects of finite angular resolution.

CoreSpacing3D implements robust algorithms to compute NN and MST edge sets and edge-length statistics in both 3D and projected 2D. It includes tools to compare edge overlap, quantify reassignment of neighbours under projection, and measure systematic changes in characteristic spacings. End-to-end Monte Carlo drivers enable ensemble analyses across many realisations, allowing users to characterise projection-induced biases as a function of intrinsic structure, spatial dynamic range, and resolution.

The package also provides user-friendly reporting utilities and plotting helpers to support exploratory analysis, figure generation, and paper preparation. In addition, it includes a public correction helper based on fitting functions presented in Barnes et al. (2026), enabling approximate inversion from observed 2D spacings to intrinsic 3D values within the calibrated regime.

This initial release establishes a stable internal API and reproducible workflow intended for research use. CoreSpacing3D is developed with clarity and extensibility in mind and is suitable for both method development and application to observational datasets.