Angleopening

Angleopening is a term used to describe the angular extent between two boundary lines or rays that share a common vertex. In geometry and related disciplines, it characterizes the opening of a wedge, aperture, or sector formed by those boundary rays.

In pure geometry, angleopening refers to the measure of the angle from one boundary ray to the other. It is typically expressed in degrees or radians. Angles can be described as undirected (magnitude only) or directed (oriented) to indicate a specific rotation from the first ray to the second, with orientations often considered modulo 360 degrees.

The concept is widely used across fields that involve directional sensing or viewing. It is common in optics and photography as a description of a lens or aperture’s opening angle, in computer graphics to specify a camera’s field of view, and in robotics or sensor design to denote the angular span of a sensor’s detection beam. In each context, a larger angleopening corresponds to a wider exposure or field, while a smaller angleopening indicates a more focused or narrow view. The term is sometimes treated as synonymous with opening angle or field of view, though precise terminology can vary by discipline.

Calculation in a mathematical setting can be done with unit direction vectors u and v for the boundary rays: the magnitude of angleopening is arccos(u · v). For a directed angle, the angle is measured from u to v according to a chosen orientation, typically modulo 360 degrees.

See also opening angle, field of view, aperture angle.