Roterad

Roterad is a Swedish adjective and past participle meaning rotated. It derives from the verb rotera, to rotate, and is used to describe objects whose orientation has been changed by rotation. The form roterad is used both attributively, as in en roterad bild (a rotated image), and predicatively, as in bilden är roterad (the image is rotated).

In language and grammar, roterad functions as a descriptive property that can refer to geometry, objects, or figures that have undergone a rotational transformation. The related present participle roterande describes the act of rotating, as in en roterande rörelse (a rotating motion).

In mathematics and computer science, roterad denotes a coordinate transformation that changes the position of points by rotating around an origin or a specified pivot. In two dimensions, a point (x, y) rotated by angle θ around the origin becomes x' = x cos θ − y sin θ and y' = x sin θ + y cos θ. In three dimensions, rotations occur around an axis and can be represented by rotation matrices, Euler angles, or quaternions, yielding a roterad configuration of points or objects. These concepts underpin tasks such as image alignment, robotics, and computer graphics.

In image processing and geographic information systems, roterade images are common when aligning scans, photographs, or maps. A rotation may be specified in degrees or radians and can be applied around a chosen pivot point, often the image center or a reference feature.

See also rotera, rotation, rotational transformation.