planeswith

planeswith is a software library for geometric computations focused on planes in three-dimensional space. It provides data structures for planes, points, lines, and vectors, and implements algorithms for common planar operations, including computing the intersection of two planes, deriving the intersection line, measuring the angle between planes, and testing for parallelism or coincidence. The library also supports projecting points onto planes, reflecting points across planes, transforming planes under rigid motions, and computing distances from points to planes.

planeswith was developed by an open-source community under the planeswith project. It gathers contributions from researchers in geometry, computer graphics, and robotics and emphasizes modularity, extensibility, and cross-language bindings. The project aims to serve education, research, and industry by providing a robust, easy-to-use toolkit for plane-based computations.

Key modules include a core geometry engine, a numerical routines module, and bindings for C++, Python, and JavaScript. The API favors high-level operations such as intersect, project, and transform, while exposing low-level linear-algebra utilities for advanced users. The library can read and write common representations of planes and can integrate with existing math stacks.

Applications include 3D graphics pipelines, computer-aided design, robotics simulation, and computational geometry education. planeswith is released under a permissive open-source license, and provides tutorials and demos to help new users. Limitations include potential numerical instability in near-degenerate configurations and performance trade-offs when compared with specialized solvers.