Vinkelspekter

Vinkelspekter is a term used to describe the distribution or set of angles that occur in a given configuration, shape or signal. It can be a discrete collection of angle values, for example a multiset of interior angles, or a continuous distribution function that describes the likelihood of different angles. The concept is used across disciplines to summarize how directions or orientations are arranged in space or in data.

In geometry, the vinkelspekter of a polygon consists of its interior angles, often listed with multiplicities. For polyhedra and other three-dimensional shapes, related angle measures include dihedral angles between adjacent faces and angles between edges and face normals. In computer vision and graphics, the distribution of edge directions or surface normals can be treated as a vinkelspekter, typically represented as histograms or probability distributions over angles.

In wave physics, optics and signal processing, a closely related idea is the angular spectrum, which describes how a wave field can be decomposed into plane waves propagating in different directions. While the angular spectrum is a technical construction in the frequency domain, it is conceptually related to the idea of a vinkelspekter as a distribution over directions.

Measurement and analysis of vinkelspekter often involve computing angles between vectors, then summarizing these angles with histograms, circular statistics (mean angle, variance) or spherical statistics in three dimensions. Applications include characterizing geometric regularity, orientation distributions in materials, edge orientation analysis in images, and directional content in optical or acoustic signals.

See also: angle distribution, angular spectrum, dihedral angle, circular statistics.