trihedron

A trihedron, in geometry and related fields, is a local reference frame in three-dimensional space formed by three directed lines (axes) that emanate from a common point. The three lines define a trihedral angle and serve as a basis for describing directions in space.

The axes need not be mutually perpendicular; a trihedron is a non-degenerate, three-directional frame. When the axes are orthogonal and of unit length, the trihedron reduces to a Cartesian or orthonormal frame, and the orientation is represented by a rotation matrix.

In use, a trihedron provides a coordinate system attached to a rigid body or a local part of space, enabling description of vectors by their components along the three axes. The orientation relative to a fixed reference frame is given by a change-of-basis matrix whose columns are the unit axis vectors.

In geometry, the term is linked to the trihedral angle—the region formed by the positive directions along the three axes. In applied domains such as robotics and computer vision, trihedra describe local attitude or pose and are often contrasted with orthonormal triads, which impose perpendicularity and equal scaling on the axes.