|
(詳細はmathematics, the axis–angle representation of a rotation parameterizes a rotation in a three-dimensional Euclidean space by three quantities, a unit vector indicating the direction of an axis of rotation, and an angle describing the magnitude of the rotation about the axis. Only two numbers, not three, are needed to define the direction of the unit vector because its magnitude is constrained. The angle scalar multiplied by the unit vector is the axis-angle vector : The vector itself does not perform rotations, but is used to construct transformations on vectors that correspond to rotations. The rotation occurs in the sense prescribed by the right-hand rule. The rotation axis is sometimes called the Euler axis. It is one of many rotation formalisms in three dimensions. The axis–angle representation is predicated on Euler's rotation theorem, which dictates that any rotation or sequence of rotations of a rigid body in a three-dimensional space is equivalent to a pure rotation about a single fixed axis. ==Rotation vector== The axis–angle representation is equivalent to the more concise rotation vector, also called the Euler vector. In this case, both the rotation axis and the angle are represented by a vector codirectional with the rotation axis whose length is the rotation angle , : It is used for the exponential and logarithm maps involving this representation. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Axis–angle representation」の詳細全文を読む スポンサード リンク
|