page_title: Orientation (geometry)
section_title: Tait–Bryan angles
hierarchical_section_title: Orientation (geometry) / Rigid body in three dimensions / Euler angles / Tait–Bryan angles
caption_attribution_description: English: Representation of how the axis and angle rotation representation can be visualized. It may not be confused with “Euler angles”.
context_page_description: In geometry, the orientation, angular position, attitude, or direction of an object such as a line, plane or rigid body is part of the description of how it is placed in the space it occupies.
  More specifically, it refers to the imaginary rotation that is needed to move the object from a reference placement to its current placement. A rotation may not be enough to reach the current placement. It may be necessary to add an imaginary translation, called the object's location. The location and orientation together fully describe how the object is placed in space. The above-mentioned imaginary rotation and translation may be thought to occur in any order, as the orientation of an object does not change when it translates, and its location does not change when it rotates.
  Euler's rotation theorem shows that in three dimensions any orientation can be reached with a single rotation around a fixed axis. This gives one common way of representing the orientation using an axis–angle representation. Other widely used methods include rotation quaternions, Euler angles, or rotation matrices.
context_section_description: These are three angles, also known as yaw, pitch and roll, Navigation angles and Cardan angles. Mathematically they constitute a set of six possibilities inside the twelve possible sets of Euler angles, the ordering being the one best used for describing the orientation of a vehicle such as an airplane. In aerospace engineering they are usually referred to as Euler angles.
caption: A rotation represented by an Euler axis and angle.
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