PSI: Constructing ad-hoc simplices to interpolate high-dimensional unstructured data
Abstract
Interpolating unstructured data using barycentric coordinates becomes infeasible at high dimensions due to the prohibitive memory requirements of building a Delaunay triangulation. We present a new algorithm to construct ad-hoc simplices that are empirically guaranteed to contain the target coordinates, based on a nearest neighbor heuristic and an iterative dimensionality reduction through projection. We use these simplices to interpolate the astrophysical cooling function Λ and show that this new approach produces good results with just a fraction of the previously required memory.
- Publication:
-
Journal of Computational Physics
- Pub Date:
- October 2022
- DOI:
- 10.1016/j.jcp.2022.111476
- arXiv:
- arXiv:2109.13926
- Bibcode:
- 2022JCoPh.46711476L
- Keywords:
-
- Geometry;
- Triangulation;
- Simplex;
- Heuristic;
- Interpolation;
- Astrophysics - Instrumentation and Methods for Astrophysics;
- Astrophysics - Cosmology and Nongalactic Astrophysics;
- Computer Science - Computational Geometry;
- Computer Science - Graphics
- E-Print:
- 4 pages, 4 figures