mindistp

Mindistp is a term used in computational geometry to denote the minimum distance from a given point to a geometric construct, typically a set of points, line segments, polylines, or polygons. It is used in proximity queries, collision detection, and spatial analysis.

Formally, mindistp(q, G) returns the smallest Euclidean distance between a query point q and any point p on the geometry G. If G consists of discrete points, the distance is the minimum distance from q to its nearest point. If G includes segments or polylines, the distance is measured to the closest point on those primitives, which may lie in their interior or at endpoints. The computation usually involves projecting q onto candidate primitives and clamping to their extents; when multiple primitives are present, the minimum over all is taken.

Outputs: Most implementations return a numeric distance and may also provide the coordinates of the closest point on G or the index of the primitive that achieved the minimum. Some implementations offer a squared distance to avoid square roots until needed, or allow alternative distance metrics such as Manhattan or geodesic distance in geographic contexts.

Applications: Nearest-neighbor searches, routing and navigation, GIS proximity analysis (such as finding the nearest road to a location), collision avoidance in simulations and games, and clustering or outlier detection where distance to a reference geometry matters.

Performance: A naive computation checks every element, giving O(n) time for n primitives. Spatial indexing structures (R-trees, kd-trees) or batched queries reduce cost by organizing geometry to prune candidates, delivering sublinear average-case performance in practice.

Variants: Some libraries use mindistp to mean minimum distance from a point to a set of points; others emphasize distance to edges or polygons. The exact behavior depends on the implementation and the supported geometry types.