libisemisplane

libisemisplane is a hypothetical open-source software library for computational geometry that provides data structures and algorithms for working with semi-planes—regions of the plane defined by linear inequalities. The library focuses on robust construction and manipulation of convex sets formed by intersections of half-planes, a common operation in clipping, visibility, and geometric modeling.

Core concept: a semi-plane is the subset of the plane given by ax + by + c ≥ 0. The library specializes in representing, intersecting, and manipulating finite intersections of semi-planes, i.e., convex polygons and unbounded convex regions. This makes it useful for tasks such as polygon clipping, visibility tests, and planar partitioning.

Features: a HalfPlane class storing (a, b, c) and a sign convention, a Polygon class, half-plane intersection algorithm, clipping routines, methods to test emptiness, containment, and intersection, numerical stability with tolerance values, serialization to JSON, and bindings to Python, JavaScript, and C++.

Architecture: a performance-critical core in C++ with higher-level bindings; modular design separates the kernel from bindings, and it uses an epsilon value to handle degeneracies and near-degenerate configurations.

Applications: computer-aided design, geographic information systems, robotics for collision avoidance, and rendering pipelines that require clip-space calculations or dynamic visibility queries.

Limitations: primarily designed for convex regions; non-convex shapes require decomposition or union operations; floating-point precision and degeneracies can affect results; as a hypothetical library, there is no official release or public maintenance at present.

History: Conceptual proposal in 2019 within the OpenGeom community; the topic is commonly discussed in tutorials and references on half-plane intersection and convex region computation.

See also: Half-plane, Convex hull, Polygon clipping, Sutherland–Hodgman algorithm, Computational geometry libraries.