normalizeAngleangle

normalizeAngleangle is a concept used in mathematics and software development to map an arbitrary angle value to a canonical representative within a fixed interval. It is commonly employed to simplify angle comparisons, accumulate rotations without unbounded growth, and maintain consistency in calculations across graphics, robotics, and simulations.

There are several common conventions for the target interval. In degrees, angles are often normalized to [0, 360) or to (-180, 180]. In radians, the equivalent intervals are [0, 2π) or (-π, π]. The choice depends on the application: [0, 2π) is convenient for full-circle wrapping, while (-π, π] is convenient for computing signed angular differences.

Algorithmically, normalization relies on the period P of the angle, which is 360 for degrees or 2π for radians. A typical implementation computes a = angle mod P; if a < 0 then a += P. The result lies in the chosen interval, often with a half-open convention such as [0, P). Special cases include handling NaN or infinite inputs and deciding how endpoints are treated (for example, whether exactly a multiple of P maps to 0 or to P, depending on the convention).

Examples: 450 degrees normalizes to 90 degrees in [0, 360); -30 degrees normalizes to 330 degrees. In radians, 7π/4 equals 315 degrees, and -π/2 normalizes to 3π/2 (in [0, 2π)). normalizeAngleangle is widely used in 3D graphics, game physics, and navigation systems to maintain stable angular values.