Pointsection

Pointsection is a concept in computational geometry and digital graphics that refers to a decomposition of a geometric object into a finite collection of simple pieces, called sections, defined with respect to one or more anchor points. In the common polygonal setting, a pointsection of a polygon P is produced by selecting a set of anchor points A on or inside P and partitioning P into subregions by drawing a prescribed set of lines or rays from each anchor and recording their intersections with the polygon boundary or with other lines. The resulting sections are pairwise disjoint and their union equals P.

Construction can follow several schemes. In a radial scheme, for each anchor a, rays are emitted at a fixed angular resolution around a; the first intersections with P's boundary (or with previously created lines) define wedge-shaped sections. In a projection-based scheme, lines are drawn from anchors toward specified directions, and the polygon is subdivided along these projections. The process is deterministic given the anchors and rules, and may be refined by increasing the angular resolution or adding more anchors.

Key properties include coverage, disjointness, and dependence on anchor placement. The partition is not unique; different sets of anchors or different angular resolutions yield different decompositions of the same object. If the subdivision uses convex wedge shapes, some sections may be convex, but convexity is not guaranteed in general.

Pointsections are used to accelerate rendering and spatial queries in graphics pipelines, to guide mesh refinement in finite element methods, and to support localized analysis in geographic information systems. The idea also informs approaches to partition-based collision detection and level-of-detail schemes. A simple example is a square with a center anchor and four rays at 0, 90, 180, and 270 degrees, producing four quadrilateral sections.