rotations.h File Reference

Header file declaring functions which convert between different representations of 3D rotation. More...

#include <dlrNumeric/quaternion.h>
#include <dlrNumeric/transform3D.h>
#include <dlrNumeric/vector3D.h>

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Namespaces
namespace	dlr
namespace	dlr::numeric
Functions
Quaternion	dlr::numeric::angleAxisToQuaternion (double angle, const Vector3D &axis, bool isNormalized=false)
	This function converts a rotation from angle-axis representation to unit quaternion representation.
Vector3D	dlr::numeric::angleAxisToRollPitchYaw (double angle, const Vector3D &axis, bool isNormalized=false)
	This function converts a rotation from angle-axis representation to roll-pitch-yaw representation.
Transform3D	dlr::numeric::angleAxisToTransform3D (double angle, const Vector3D &axis, bool isNormalized=false)
	This function converts a rotation from angle-axis representation to Transform3D representation.
std::pair< double, Vector3D >	dlr::numeric::quaternionToAngleAxis (const Quaternion &quaternion)
	This function converts a rotation from Quaternion representation to Angle-Axis representation.
Vector3D	dlr::numeric::quaternionToRollPitchYaw (const Quaternion &quaternion)
	This function converts a rotation from Quaternion representation to Roll-Pitch-Yaw representation.
Transform3D	dlr::numeric::quaternionToTransform3D (const Quaternion &quaternion)
	This function converts a rotation from Quaternion representation to Transform3D representation.
std::pair< double, Vector3D >	dlr::numeric::rollPitchYawToAngleAxis (const Vector3D &rollPitchYaw)
	This function converts a rotation from Roll-Pitch-Yaw representation to Angle-Axis representation.
Quaternion	dlr::numeric::rollPitchYawToQuaternion (const Vector3D &rollPitchYaw)
	This function converts a rotation from Roll-Pitch-Yaw representation to Quaternion representation.
Transform3D	dlr::numeric::rollPitchYawToTransform3D (const Vector3D &rollPitchYaw)
	This function converts a rotation from Roll-Pitch-Yaw representation to Transform3D representation.
std::pair< double, Vector3D >	dlr::numeric::transform3DToAngleAxis (const Transform3D &transform3D)
	This function converts a rotation from Transform3D representation to Angle-Axis representation.
Quaternion	dlr::numeric::transform3DToQuaternion (const Transform3D &transform3D)
	This function converts a rotation from Transform3D representation to Quaternion representation.
Vector3D	dlr::numeric::transform3DToRollPitchYaw (const Transform3D &transform3D)
	This function converts a rotation from Transform3D representation to Roll-Pitch-Yaw representation.

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Detailed Description

Header file declaring functions which convert between different representations of 3D rotation.

Copyright (C) 2005-2007 David LaRose, dlr@cs.cmu.edu See accompanying file, LICENSE.TXT, for details.

The functions in this file deal with several different ways of representing 3D rotation, which are described here:

• Angle-Axis representation is specified by a double and a Vector3D instance. The double specifies the size of the rotation in radians. Positive numbers mean clockwise rotation as you look from the origin along the axis of rotation. Negative numbers mean counter-clockwise rotation. The Vector3D instance specifies the axis of rotation.

• Unit Quaternion representation uses a single Quaternion instance. For a given rotation, alpha, around the unit axis [x, y, z], the corresponding unit quaternion representation is Quaternion(cos(alpha/2.0), sin(alpha/2.0) * x, sin(alpha/2.0) * y, sin(alpha/2.0) * z).

• Roll-Pitch-Yaw representation specifies a 3D rotation as consecutive rotations around the three axes. Roll, pitch, and yaw are all specified in radians. The 3D rotation is obtained by first rotation to the yaw angle around the Z axis, then rotating to the pitch angle around the new Y axis, and finally rotating to the Roll angle around the X axis.

• Transform3D representation specifies a 3D rotation using a coordinate transformation matrix. Only the upper-left 3x3 sub-matrix is considered. In order to be a valid rotation matrix, the rows (and therefore columns) of this 3x3 sub-matrix must be orthonormal. Note that no attempt is made to check for this condition, or to correct for non-orthonormal matrices. If you pass an invalid rotation matrix to any of these routines, the results are undefined.

Revision

880

Date

2007-05-04 00:33:49 -0400 (Fri, 04 May 2007)

Definition in file rotations.h.

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