segmentswithout

Segmentswithout is a term used in computational geometry and vector graphics to describe an operation that removes certain line segments from a collection. Specifically, given a set S of segments and a predicate P defined on segments, segmentswithout(S, P) yields the subset of S consisting of all segments s for which P(s) is false. In other words, it implements the set difference relative to a predicate: segmentswithout(S, P) = { s in S | not P(s) }.

In programming contexts, segmentswithout is often implemented as a filter or as a use of a higher-order function that tests each segment against P. The choice of predicate determines the outcome; common examples include removing segments that intersect a region, that lie outside a bounding box, or that have zero length. The operation is typically agnostic to the dimensionality of the space, though most common use cases involve two- or three-dimensional geometry.

Performance and implementation notes vary with the cost of evaluating P. If P is constant-time, the operation runs in linear time with respect to the number of segments, O(n), and uses additional memory proportional to the size of the resulting subset. If P requires spatial queries, overall complexity depends on the data structures used for the predicate evaluations, such as spatial indices or sweep-line algorithms.

Applications of segmentswithout include data cleaning in geographic information systems, preparation of vector graphics for rendering, and preprocessing steps in clipping or tiling algorithms where unwanted segments must be discarded before further processing.

See also: filter, clip, set difference, geometric predicates, polygon clipping.