Trirectangular Trihedral

a figure formed by three mutually perpendicular rays that issue from a common point. Sometimes a trirectangular trihedral is defined as a system of three mutually perpendicular unit vectors originating at the same point.

Trirectangular trihedrals selected in a special way play an important role in mechanics (in the study of relative motion) and in the differential geometry of curves and surfaces. In the theory of space curves the notion of the moving trihedral of a curve is of great importance. The moving trihedral of a curve is the configuration consisting of the vector t directed along the tangent to the curve at a variable point of the curve, the vector n directed along the principal normal to the curve at the variable point, and the vector b directed along the binormal to the curve at the variable point.