nonselfintersection

Nonselfintersection refers to the property of a curve, polyline, or polygon that it does not cross or touch itself, except in cases allowed by the definition (such as the endpoints of a closed curve meeting). In the plane, a non-self-intersecting curve can be described as visits to points along its path without repeated interior points; a closed non-self-intersecting curve may start and end at the same point.

Common examples include a straight line segment, a circle, or a simple polygon whose edges meet only at shared vertices in the natural adjacency and do not cross elsewhere. By contrast, figures such as the figure-eight or a polygon with crossing edges are self-intersecting and do not possess this property. In geometry and graphics, the term simple is often used for non-self-intersecting curves or polygons.

In the plane, the Jordan curve theorem has particular relevance for simple closed curves: such a curve partitions the plane into an interior region and an exterior region. Simple polygons inherit well-defined interiors, enabling operations like area calculation, filling, and rendering.

In computer science and computational geometry, detecting nonselfintersection is a common preprocessing step. Algorithms may test all segment pairs for intersections or use sweep-line techniques to achieve near-linearithmic time complexity. Ensuring non-self-intersection is important in vector graphics, font rendering, GIS polygon handling, and path planning, where self-intersections can complicate shading, routing, or spatial queries.

In higher dimensions, a non-self-intersecting curve is an embedding of an interval or circle into space, while self-intersections correspond to crossings or singularities.