From d5052f1c296dddf51b3e83d59bf3e3c1952cb2d0 Mon Sep 17 00:00:00 2001 From: cathook Date: Sun, 1 Jun 2014 13:56:57 +0800 Subject: big chnage --- doc/html/classmeow_1_1Rotation3D.html | 928 ++++++++++++++++++++++++++++++++++ 1 file changed, 928 insertions(+) create mode 100644 doc/html/classmeow_1_1Rotation3D.html (limited to 'doc/html/classmeow_1_1Rotation3D.html') diff --git a/doc/html/classmeow_1_1Rotation3D.html b/doc/html/classmeow_1_1Rotation3D.html new file mode 100644 index 0000000..5ccce18 --- /dev/null +++ b/doc/html/classmeow_1_1Rotation3D.html @@ -0,0 +1,928 @@ + + + + + + + +Templates -- Meow: meow::Rotation3D< Scalar > Class Template Reference + + + + + + + + + + + +
+
+ + + + + + + +
+
Templates -- Meow +  1.1.2 +
+
不能,也不應該先編譯成obj-file的templates
+
+
+ + +
+
+ +
+
+
+ +
+
+
+Classes | +Public Member Functions | +List of all members
+
+
meow::Rotation3D< Scalar > Class Template Reference
+
+
+ +

Rotation a point/vector alone an axis with given angle in 3D world. + More...

+ +

#include "LinearTransformations.h"

+
+Inheritance diagram for meow::Rotation3D< Scalar >:
+
+
+ + +meow::LinearTransformation< Scalar > +meow::Transformation< Scalar > + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+Public Member Functions

 Rotation3D ()
 
 Rotation3D (Rotation3D const &b)
 
 ~Rotation3D ()
 
Rotation3D & copyFrom (Rotation3D const &b)
 Copy data. More...
 
Rotation3D & referenceFrom (Rotation3D const &b)
 Reference data. More...
 
Scalar parameter (size_t i) const
 same as theta(i) More...
 
Scalar parameter (size_t i, Scalar const &s)
 same as theta(i, s) More...
 
Scalar const & theta (size_t i) const
 Get the i -th theta. More...
 
Scalar const & theta (size_t i, Scalar const &s)
 Set the i -th theta. More...
 
void axisAngle (Vector< Scalar > const &axis, Scalar const &angle)
 Setting. More...
 
Rotation3D & add (Rotation3D const &r)
 Concat another rotation transformation. More...
 
Matrix< Scalar > transformate (Matrix< Scalar > const &x) const
 Do the transformate. More...
 
Matrix< Scalar > jacobian (Matrix< Scalar > const &x) const
 Return the jacobian matrix (derivate by the input vector) of this transformate. More...
 
Matrix< Scalar > jacobian (Matrix< Scalar > const &x, size_t i) const
 Return the jacobian matrix of this transformate. More...
 
Matrix< Scalar > transformateInv (Matrix< Scalar > const &x) const
 Do the inverse transformate. More...
 
Matrix< Scalar > jacobianInv (Matrix< Scalar > const &x) const
 Return the jacobian matrix of the inverse form of this transformate. More...
 
Matrix< Scalar > jacobianInv (Matrix< Scalar > const &x, size_t i) const
 Return the jacobian matrix of the inverse form of this transformate. More...
 
Matrix< Scalar > matrixInv () const
 Return the inverse matrix. More...
 
Rotation3D & operator= (Rotation3D const &b)
 same as copyFrom(b) More...
 
- Public Member Functions inherited from meow::LinearTransformation< Scalar >
virtual ~LinearTransformation ()
 
virtual Matrix< Scalar > const & matrix () const
 Return the matrix form of this transformation. More...
 
- Public Member Functions inherited from meow::Transformation< Scalar >
virtual ~Transformation ()
 
size_t inputRows () const
 Return the number of rows of the input matrix. More...
 
size_t inputCols () const
 Return the number of columns of the input matrix. More...
 
size_t outputRows () const
 Return the number of rows of the output matrix. More...
 
size_t outputCols () const
 Return the number of columns of the output matrix. More...
 
size_t parameterSize () const
 Return the number of parameters. More...
 
virtual bool inversable () const
 Return whether this transformation is inversable or not. More...
 
+ + + + + + + + + + + + + + + + + +

+Additional Inherited Members

- Protected Member Functions inherited from meow::LinearTransformation< Scalar >
 LinearTransformation (size_t inputRows, size_t outputRows, size_t psize)
 
 LinearTransformation (size_t inputRows, size_t outputRows, size_t psize, Matrix< Scalar > const &m)
 
 LinearTransformation (LinearTransformation const &b)
 
LinearTransformation & copyFrom (LinearTransformation const &b)
 Copy settings, matrix from another LinearTransformation. More...
 
LinearTransformation & referenceFrom (LinearTransformation const &b)
 Reference settings, matrix from another LinearTransformation. More...
 
Matrix< Scalar > const & matrix (Matrix< Scalar > const &m)
 Setup the matrix. More...
 
+

Detailed Description

+

template<class Scalar>
+class meow::Rotation3D< Scalar >

+ +

Rotation a point/vector alone an axis with given angle in 3D world.

+
Author
cat_leopard
+

Constructor & Destructor Documentation

+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + +
meow::Rotation3D< Scalar >::Rotation3D ()
+ 		+inline
+
+

Constructor with no rotation

+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + +
meow::Rotation3D< Scalar >::Rotation3D (Rotation3D< Scalar > const & b)
+ 		+inline
+
+

Constructor and copy data

+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + +
meow::Rotation3D< Scalar >::~Rotation3D ()
+ 		+inline
+
+

Destructor

+ +
+
+

Member Function Documentation

+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + +
Rotation3D& meow::Rotation3D< Scalar >::add (Rotation3D< Scalar > const & r)
+ 		+inline
+
+ +

Concat another rotation transformation.

+
Parameters
+ + +
[in]ranother rotation transformation
+
+
+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + + + + + + + + + + + +
void meow::Rotation3D< Scalar >::axisAngle (Vector< Scalar > const & axis,
Scalar const & angle 
)
+ 		+inline
+
+ +

Setting.

+
Parameters
+ + + +
[in]axisaxis
[in]angleangle
+
+
+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + +
Rotation3D& meow::Rotation3D< Scalar >::copyFrom (Rotation3D< Scalar > const & b)
+ 		+inline
+
+ +

Copy data.

+
Parameters
+ + +
[in]banother Rotation3D class.
+
+
+
Returns
*this
+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + +
Matrix<Scalar> meow::Rotation3D< Scalar >::jacobian (Matrix< Scalar > const & x) const
+ 		+inlinevirtual
+
+ +

Return the jacobian matrix (derivate by the input vector) of this transformate.

+

The matrix we return is:

+

+\[ \left[ \begin{array}{ccc} 2(n_x^2 - 1) \sin^2\phi + 1 & 2n_x n_y \sin^2\phi - 2n_z\cos \phi\sin \phi & 2n_x n_z \sin^2\phi + 2n_y\cos \phi\sin \phi \\ 2n_y n_x \sin^2\phi + 2n_z\cos \phi\sin \phi & 2(n_y^2 - 1) \sin^2\phi + 1 & 2n_y n_z \sin^2\phi - 2n_x\cos \phi\sin \phi \\ 2n_z n_x \sin^2\phi - 2n_y\cos \phi\sin \phi & 2n_z n_y \sin^2\phi + 2n_x\cos \phi\sin \phi & 2(n_z^2 - 1) \sin^2\phi + 1 \\ \end{array} \right] \] +

+

Where the definition of $ \vec{n} $ and $ \phi $ is the same as the definition in the description of the method transformate() .

+
Parameters
+ + +
[in]xthe input vector (in this case it is a useless parameter)
+
+
+
Returns
a matrix
+ +

Reimplemented from meow::Transformation< Scalar >.

+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + + + + + + + + + + + +
Matrix<Scalar> meow::Rotation3D< Scalar >::jacobian (Matrix< Scalar > const & x,
size_t i 
) const
+ 		+inlinevirtual
+
+ +

Return the jacobian matrix of this transformate.

+

Here we need to discussion in three case:

+
    +
  • i = 0, derivate by the x axis of the vector theta

    +\[ \left[ \begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & -1 \\ 0 & 1 & 0 \\ \end{array} \right] \left[ \begin{array}{ccc} 2(n_x^2 - 1) \sin^2\phi + 1 & 2n_x n_y \sin^2\phi - 2n_z\cos \phi\sin \phi & 2n_x n_z \sin^2\phi + 2n_y\cos \phi\sin \phi \\ 2n_y n_x \sin^2\phi + 2n_z\cos \phi\sin \phi & 2(n_y^2 - 1) \sin^2\phi + 1 & 2n_y n_z \sin^2\phi - 2n_x\cos \phi\sin \phi \\ 2n_z n_x \sin^2\phi - 2n_y\cos \phi\sin \phi & 2n_z n_y \sin^2\phi + 2n_x\cos \phi\sin \phi & 2(n_z^2 - 1) \sin^2\phi + 1 \\ \end{array} \right] \left[ \begin{array}{c} x \\ y \\ z \\ \end{array} \right] \] +

    +
    • +
  • i = 1, derivate by the y axis of the vector theta

    +\[ \left[ \begin{array}{ccc} 0 & 0 & 1 \\ 0 & 0 & 0 \\ -1 & 0 & 0 \\ \end{array} \right] \left[ \begin{array}{ccc} 2(n_x^2 - 1) \sin^2\phi + 1 & 2n_x n_y \sin^2\phi - 2n_z\cos \phi\sin \phi & 2n_x n_z \sin^2\phi + 2n_y\cos \phi\sin \phi \\ 2n_y n_x \sin^2\phi + 2n_z\cos \phi\sin \phi & 2(n_y^2 - 1) \sin^2\phi + 1 & 2n_y n_z \sin^2\phi - 2n_x\cos \phi\sin \phi \\ 2n_z n_x \sin^2\phi - 2n_y\cos \phi\sin \phi & 2n_z n_y \sin^2\phi + 2n_x\cos \phi\sin \phi & 2(n_z^2 - 1) \sin^2\phi + 1 \\ \end{array} \right] \left[ \begin{array}{c} x \\ y \\ z \\ \end{array} \right] \] +

    +
    • +
  • i = 2, derivate by the z axis of the vector theta

    +\[ \left[ \begin{array}{ccc} 0 & -1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \\ \end{array} \right] \left[ \begin{array}{ccc} 2(n_x^2 - 1) \sin^2\phi + 1 & 2n_x n_y \sin^2\phi - 2n_z\cos \phi\sin \phi & 2n_x n_z \sin^2\phi + 2n_y\cos \phi\sin \phi \\ 2n_y n_x \sin^2\phi + 2n_z\cos \phi\sin \phi & 2(n_y^2 - 1) \sin^2\phi + 1 & 2n_y n_z \sin^2\phi - 2n_x\cos \phi\sin \phi \\ 2n_z n_x \sin^2\phi - 2n_y\cos \phi\sin \phi & 2n_z n_y \sin^2\phi + 2n_x\cos \phi\sin \phi & 2(n_z^2 - 1) \sin^2\phi + 1 \\ \end{array} \right] \left[ \begin{array}{c} x \\ y \\ z \\ \end{array} \right] \] +

    +
    • +
+

Where $ (x,y,z) $ is the input vector, $ \vec{n}, \phi $ is the same one in the description of transformate().

+
Parameters
+ + + +
[in]xthe input vector
[in]ithe index of the parameters(theta) to dervite
+
+
+
Returns
a matrix
+ +

Reimplemented from meow::Transformation< Scalar >.

+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + +
Matrix<Scalar> meow::Rotation3D< Scalar >::jacobianInv (Matrix< Scalar > const & x) const
+ 		+inlinevirtual
+
+ +

Return the jacobian matrix of the inverse form of this transformate.

+
Parameters
+ + +
[in]xthe input vector
+
+
+
Returns
a matrix
+ +

Reimplemented from meow::Transformation< Scalar >.

+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + + + + + + + + + + + +
Matrix<Scalar> meow::Rotation3D< Scalar >::jacobianInv (Matrix< Scalar > const & x,
size_t i 
) const
+ 		+inlinevirtual
+
+ +

Return the jacobian matrix of the inverse form of this transformate.

+
Parameters
+ + + +
[in]xthe input vector
[in]ithe index of the parameters(theta) to dervite
+
+
+
Returns
a matrix
+ +

Reimplemented from meow::Transformation< Scalar >.

+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + +
Matrix<Scalar> meow::Rotation3D< Scalar >::matrixInv () const
+ 		+inlinevirtual
+
+ +

Return the inverse matrix.

+

In this case, the inverse matrix is equal to the transpose of the matrix

+
Returns
a matrix
+ +

Reimplemented from meow::LinearTransformation< Scalar >.

+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + +
Rotation3D& meow::Rotation3D< Scalar >::operator= (Rotation3D< Scalar > const & b)
+ 		+inline
+
+ +

same as copyFrom(b)

+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + +
Scalar meow::Rotation3D< Scalar >::parameter (size_t i) const
+ 		+inlinevirtual
+
+ +

same as theta(i)

+ +

Implements meow::Transformation< Scalar >.

+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + + + + + + + + + + + +
Scalar meow::Rotation3D< Scalar >::parameter (size_t i,
Scalar const & s 
)
+ 		+inlinevirtual
+
+ +

same as theta(i, s)

+ +

Implements meow::Transformation< Scalar >.

+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + +
Rotation3D& meow::Rotation3D< Scalar >::referenceFrom (Rotation3D< Scalar > const & b)
+ 		+inline
+
+ +

Reference data.

+
Parameters
+ + +
[in]banother Rotation3D class.
+
+
+
Returns
*this
+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + +
Scalar const& meow::Rotation3D< Scalar >::theta (size_t i) const
+ 		+inline
+
+ +

Get the i -th theta.

+

i can only be 1, 2 or 3

+
Parameters
+ + +
[in]iindex
+
+
+
Returns
i -th theta
+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + + + + + + + + + + + +
Scalar const& meow::Rotation3D< Scalar >::theta (size_t i,
Scalar const & s 
)
+ 		+inline
+
+ +

Set the i -th theta.

+

i can only be 1, 2 or 3

+
Parameters
+ + + +
[in]iindex
[in]snew theta value
+
+
+
Returns
i -th theta
+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + +
Matrix<Scalar> meow::Rotation3D< Scalar >::transformate (Matrix< Scalar > const & x) const
+ 		+inlinevirtual
+
+ +

Do the transformate.

+

Assume:

+
    +
  • The input vector is $ (x ,y ,z ) $
    • +
  • The output vector is $ (x',y',z') $
    • +
  • The parameters theta is $ \vec{\theta}=(\theta_x,\theta_y,\theta_z) $
    • +
+

Then we have:

+

+\[ \left[ \begin{array}{c} x' \\ y' \\ z' \\ \end{array} \right] = \left[ \begin{array}{ccc} 2(n_x^2 - 1) \sin^2\phi + 1 & 2n_x n_y \sin^2\phi - 2n_z\cos \phi\sin \phi & 2n_x n_z \sin^2\phi + 2n_y\cos \phi\sin \phi \\ 2n_y n_x \sin^2\phi + 2n_z\cos \phi\sin \phi & 2(n_y^2 - 1) \sin^2\phi + 1 & 2n_y n_z \sin^2\phi - 2n_x\cos \phi\sin \phi \\ 2n_z n_x \sin^2\phi - 2n_y\cos \phi\sin \phi & 2n_z n_y \sin^2\phi + 2n_x\cos \phi\sin \phi & 2(n_z^2 - 1) \sin^2\phi + 1 \\ \end{array} \right] \left[ \begin{array}{c} x \\ y \\ z \\ \end{array} \right] \] +

+

Where:

+
    +
  • $ \phi $ is the helf of length of $ \vec{\theta} $ , which means $ \phi = \frac{\left|\vec{\theta}\right|}{2} = \frac{1}{2}\sqrt{\theta_x^2 + \theta_y^2 + \theta_z^2} $
    • +
  • $ \vec{n} $ is the normalized form of $ \vec{\theta} $ , which means $ \vec{n} = (n_x,n_y,n_z) = \vec{\theta} / 2\phi $
    • +
+
Parameters
+ + +
[in]xthe input vector
+
+
+
Returns
the output matrix
+ +

Implements meow::Transformation< Scalar >.

+ +
+
+ +
+
+
+template<class Scalar>
+ + + + + +
+ + + + + + + + +
Matrix<Scalar> meow::Rotation3D< Scalar >::transformateInv (Matrix< Scalar > const & x) const
+ 		+inlinevirtual
+
+ +

Do the inverse transformate.

+
Parameters
+ + +
[in]xthe input vector
+
+
+
Returns
the output vector
+ +

Reimplemented from meow::Transformation< Scalar >.

+ +
+
+
The documentation for this class was generated from the following file: +
+
+ + + + + -- cgit v1.2.3