#include <rtcRotation.h>
Public Member Functions | |
| void | apply (Vec3< T > &v) const |
| Helper for applying the rotation to points: Rotation * Vec. | |
| Vec3< T > | apply (const Vec3< T > &v) const |
| Rotation () | |
| Constructor. | |
| Rotation (const T x11, const T x12, const T x13, const T x21, const T x22, const T x23, const T x31, const T x32, const T x33) | |
| Rotation (const Mat< T, 3, 3 > &m) | |
| Rotation (const Quaternion< T > &q) | |
| Rotation (const EulerAngles< T > &e) | |
| template<class U > | |
| Rotation (const Mat< U, 3, 3 > &m) | |
| Casting Operation. | |
| void | set (const Quaternion< T > &q) |
| Mutators. | |
| void | set (const EulerAngles< T > &e) |
| void | set (const T theta, const T phi) |
Detailed Description
template<class T>
class rtc::Rotation< T >
The Rotation Matrix Class
Defines rotation matrix class that derives from SMat<T,3> and knows how to construct itself from several other common rotation representations, such as quaternions, axis angles, and euler angles.
A coordinate rotation is a rotation about a single coordinate axis. Enumerating the x-, y-, and z-axes with 1,2, and 3, the coordinate rotations are:
![\[ R_{1}=\left[\begin{array}{ccc} 1 & 0 & 0\\ 0 & \cos\left(\phi\right) & -\sin\left(\phi\right)\\ 0 & \sin\left(\phi\right) & \cos\left(\phi\right)\end{array}\right] \]](form_0.png)
![\[ R_{2}=\left[\begin{array}{ccc} \cos\left(\theta\right) & 0 & \sin\left(\theta\right)\\ 0 & 1 & 0\\ -\sin\left(\theta\right) & 0 & \cos\left(\theta\right)\end{array}\right] \]](form_1.png)
![\[ R_{3}=\left[\begin{array}{ccc} \cos\left(\psi\right) & -\sin\left(\psi\right) & 0\\ \sin\left(\psi\right) & \cos\left(\psi\right) & 0\\ 0 & 0 & 1\end{array}\right] \]](form_2.png)
A matrix representing the end result of all three rotations is formed by successive multiplication of the matrices representing the three simple rotations, as in the equation
![\[ R_{3}R_{2}R_{1}=\left[\begin{array}{ccc} \cos\left(\psi\right)\cos\left(\theta\right) & \cos\left(\psi\right)\sin\left(\theta\right)\sin\left(\phi\right)-\sin\left(\psi\right)\cos\left(\phi\right) & \cos\left(\psi\right)\sin\left(\theta\right)\cos\left(\phi\right)+\sin\left(\psi\right)\sin\left(\phi\right)\\ \sin\left(\psi\right)\cos\left(\theta\right) & \sin\left(\psi\right)\sin\left(\theta\right)\sin\left(\phi\right)+\cos\left(\psi\right)\cos\left(\phi\right) & \sin\left(\psi\right)\sin\left(\theta\right)\cos\left(\phi\right)-\cos\left(\psi\right)\sin\left(\phi\right)\\ -\sin\left(\theta\right) & \cos\left(\theta\right)\sin\left(\phi\right) & \cos\left(\theta\right)\cos\left(\phi\right)\end{array}\right] \]](form_3.png)
Definition at line 75 of file rtcRotation.h.
Constructor & Destructor Documentation
| rtc::Rotation< T >::Rotation | ( | ) | [inline] |
Constructor.
Ctor that intializes to an identity rotation matrix.
Definition at line 116 of file rtcRotation.h.
| rtc::Rotation< T >::Rotation | ( | const T | x11, |
| const T | x12, | ||
| const T | x13, | ||
| const T | x21, | ||
| const T | x22, | ||
| const T | x23, | ||
| const T | x31, | ||
| const T | x32, | ||
| const T | x33 | ||
| ) | [inline] |
Ctor that initializes matrix entries directly.
Definition at line 124 of file rtcRotation.h.
| rtc::Rotation< T >::Rotation | ( | const Mat< T, 3, 3 > & | m | ) | [inline] |
Ctor that initializes from Mat<T,3,3>.
Definition at line 135 of file rtcRotation.h.
| rtc::Rotation< T >::Rotation | ( | const Quaternion< T > & | q | ) | [inline] |
Ctor that builds a rotation matrix from a quaternion Precondition: quaternion must have unit norm for matrix to have unit norm
Definition at line 141 of file rtcRotation.h.
| rtc::Rotation< T >::Rotation | ( | const EulerAngles< T > & | e | ) | [inline] |
Ctor that builds a rotation matrix from euler angles
Definition at line 148 of file rtcRotation.h.
| rtc::Rotation< T >::Rotation | ( | const Mat< U, 3, 3 > & | m | ) | [inline] |
Casting Operation.
Casting Ctor that initializes from a Mat<U,3,3> with type cast
Definition at line 155 of file rtcRotation.h.
Member Function Documentation
| void rtc::Rotation< T >::apply | ( | Vec3< T > & | v | ) | const [inline] |
| Vec3< T > rtc::Rotation< T >::apply | ( | const Vec3< T > & | v | ) | const [inline] |
Helper for applying the rotation to points: Rotation * Vec3
Definition at line 211 of file rtcRotation.h.
| void rtc::Rotation< T >::set | ( | const Quaternion< T > & | q | ) | [inline] |
Mutators.
Set the rotation matrix according to passed quaternion Precondition: quaternion must have unit norm for matrix to have unit norm
Definition at line 163 of file rtcRotation.h.
| void rtc::Rotation< T >::set | ( | const EulerAngles< T > & | e | ) | [inline] |
Set the rotation matrix according to passed euler angles
Definition at line 178 of file rtcRotation.h.
| void rtc::Rotation< T >::set | ( | const T | theta, |
| const T | phi | ||
| ) | [inline] |
Set the rotation matrix according to passed 2 angles
Definition at line 196 of file rtcRotation.h.
The documentation for this class was generated from the following file: