Struct for holding information about a rigid transform. Note that rotation R = Rx*Ry*Rz, where Rx, Ry, and Rz are the rotations about x, y and z aaxes, and the angles are stored (in radians) in the rotation member. More...

#include <registration.h>

Public Member Functions
	Rigid3DTrans ()

void	invert ()
	Inverts rigid transform, where: More...

Matrix3d	rotMatrix ()
	Constructs and returns rotation Matrix. More...

void	setRotation (const Matrix3d &rot)
	Constructs rotation vector from rotation matrix. More...

void	toRASCoords (ptr< const MRImage > in)
	Converts to world coordinates based on the orientation stored in input image. More...

void	toIndexCoords (ptr< const MRImage > in, bool forcegridcenter)
	Converts from world coordinates to index coordinates based on the orientation stored in input image. More...

Public Attributes
Vector3d	rotation

Vector3d	shift

Vector3d	center

bool	ras_coord
	Indicates the stored transform is relative to physical coordintes rather than index coordinates. More...

Detailed Description

Struct for holding information about a rigid transform. Note that rotation R = Rx*Ry*Rz, where Rx, Ry, and Rz are the rotations about x, y and z aaxes, and the angles are stored (in radians) in the rotation member.

$\hat y = R(\hat x- \hat c)+ \hat s+ \hat c$

Definition at line 855 of file registration.h.

Constructor & Destructor Documentation

npl::Rigid3DTrans::Rigid3DTrans ( )

inline

Definition at line 867 of file registration.h.

Member Function Documentation

void npl::Rigid3DTrans::invert ( )

Inverts rigid transform, where:

Original: $\hat y = R(\hat x- \hat c)+ \hat s+ \hat c$

Inverse: $\hat x = R^{-1}(\hat y - \hat s - \hat c) + \hat c$

So the new parameters, interms of the old are:

$\hat c' = \hat s+ \hat c$

$\hat s' = -\hat s$

$\hat R' = R^{-1}$

Matrix3d npl::Rigid3DTrans::rotMatrix ( )

Constructs and returns rotation Matrix.

Returns: Rotation matrix

void npl::Rigid3DTrans::setRotation ( const Matrix3d & rot )

Constructs rotation vector from rotation matrix.

Parameters

rot	Rotation matrix

void npl::Rigid3DTrans::toIndexCoords	(	ptr< const MRImage >	in,
		bool	forcegridcenter
	)

Converts from world coordinates to index coordinates based on the orientation stored in input image.

The center of rotation is assumed to be the center of the grid which is (SIZE-1)/2 in each dimension.

The Rotation ( $R$ ) and Shift( $\hat s$ ) are given by:

$\begin{eqnarray*} R &=& A^{-1}QA \\ \hat s &=& R\hat c -\hat c - A^{-1}(\hat b + Q\hat b - Q\hat d + \hat t + \hat d ) \end{eqnarray*}$

where $A$ is the rotation of the grid, $\hat c$ is the center of the grid, $\hat b$ is the origin of the grid, $ Q $ is the rotation matrix in RAS coordinate space, $\hat d$ is the given center of roation (in RAS coordinates), and $\hat t$ is the original shift in RAS coordinates.

Parameters

in	Source of index->world transform
forcegridcenter	Force the center to be the center of the grid rather than using the location corresponding to the current center

void npl::Rigid3DTrans::toRASCoords ( ptr< const MRImage > in )

Converts to world coordinates based on the orientation stored in input image.

For a rotation in RAS coordinates, with rotation $Q$ , shift $t$ and center $d$ :