#include <HomogeneousTransform.hh>

Public Types
typedef T	value_type

Public Member Functions
	HomogeneousTransform ()
	Default constructor: axis aligned with the global coordinate frame and the point located at the origin. More...

	HomogeneousTransform (xyzVector< T > const &p1, xyzVector< T > const &p2, xyzVector< T > const &p3)
	Construct the coordinate frame from the points defined such that. More...

	HomogeneousTransform (xyzVector< T > const &xaxis, xyzVector< T > const &yaxis, xyzVector< T > const &zaxis, xyzVector< T > const &point)
	Constructor from xyzVectors: trust that the axis are indeed orthoganol. More...

	HomogeneousTransform (xyzMatrix< T > const &axes, xyzVector< T > const &point)
	Constructor from an xyzMatrix and xyzVectors: trust that the axis are indeed orthoganol. More...

value_type	xx () const

value_type	xy () const

value_type	xz () const

value_type	yx () const

value_type	yy () const

value_type	yz () const

value_type	zx () const

value_type	zy () const

value_type	zz () const

value_type	px () const

value_type	py () const

value_type	pz () const

xyzVector< T >	xaxis () const

xyzVector< T >	yaxis () const

xyzVector< T >	zaxis () const

xyzVector< T >	point () const

xyzMatrix< T >	rotation_matrix () const

void	set_identity_rotation ()
	Mutators. More...

void	set_identity_transform ()

void	set_identity ()

void	set_xaxis_rotation_deg (T angle)

void	set_yaxis_rotation_deg (T angle)

void	set_zaxis_rotation_deg (T angle)

void	set_xaxis_rotation_rad (T angle)

void	set_yaxis_rotation_rad (T angle)

void	set_zaxis_rotation_rad (T angle)

void	set_transform (xyzVector< T > const &t)
	Set this HT to describe a transformation along the three axes. This has the size effect of setting the axes to the global axes. More...

void	set_point (xyzVector< T > const &p)
	Set the point that this HT is centered at. This leaves the axes untouched. More...

void	walk_along_x (T delta)
	Right multiply this coordinate frame by the frame 1 0 0 delta 0 1 0 0 0 0 1 0. More...

void	walk_along_y (T delta)
	Right multiply this coordinate frame by the frame 1 0 0 0 0 1 0 delta 0 0 1 0. More...

void	walk_along_z (T delta)
	Right multiply this coordinate frame by the frame 1 0 0 0 0 1 0 0 0 0 1 delta. More...

HomogeneousTransform< T >	operator* (HomogeneousTransform< T > const &rmat) const
	Multiplication. More...

xyzVector< T >	operator* (xyzVector< T > const &vect) const
	Transform a point. The input point is a location in this coordinate frame the output point is the location in global coordinate frame. More...

HomogeneousTransform< T >	inverse () const
	Invert this matrix. More...

xyzVector< T >	to_local_coordinate (xyzVector< T > const &v) const
	Convert a point in the global coordinate system to a point in this coordinate frame. If this frame is F and the point is p, then this solves for x st: F x = p. Equivalent to computing (F.inverse() * p).point(). More...

xyzVector< T >	euler_angles_rad () const
	Return the three euler angles (in radians) that describe this HomogeneousTransform as the series of a Z axis rotation by the angle phi (returned in position 1 of the output vector), followed by an X axis rotation by the angle theta (returned in position 3 of the output vector), followed by another Z axis rotation by the angle psi (returned in position 2 of the output vector). This code is a modified version of Alex Z's code from r++. More...

xyzVector< T >	euler_angles_deg () const

void	from_euler_angles_rad (xyzVector< T > const &euler)
	Construct the coordinate frame from three euler angles that describe the frame. Keep the point fixed. See the description for euler_angles_rad() to understand the Z-X-Z transformation convention. More...

void	from_euler_angles_deg (xyzVector< T > const &euler)

T	xform_magnitude (T radius_of_gyration)
	Less accurate functions. More...

std::ostream &	show (std::ostream &stream=std::cout) const

Private Member Functions
bool	orthonormal () const

bool	orthoganol () const
	Are the axis orthoganol. More...

bool	normal () const
	Are the axis of unit length? More...

Private Attributes
value_type	xx_
	For axis Q, the R component is named qr_; e.g. The Z component of the Y axis is yz_;. More...

value_type	yx_

value_type	zx_

value_type	px_

value_type	xy_

value_type	yy_

value_type	zy_

value_type	py_

value_type	xz_

value_type	yz_

value_type	zz_

value_type	pz_

Member Typedef Documentation

template<class T>

typedef T numeric::HomogeneousTransform< T >::value_type

Constructor & Destructor Documentation

template<class T>

numeric::HomogeneousTransform< T >::HomogeneousTransform ( )

inline

Default constructor: axis aligned with the global coordinate frame and the point located at the origin.

template<class T>

numeric::HomogeneousTransform< T >::HomogeneousTransform	(	xyzVector< T > const &	p1,
		xyzVector< T > const &	p2,
		xyzVector< T > const &	p3
	)

inline

Construct the coordinate frame from the points defined such that.

the point is at p3,
the z axis points along p2 to p3.
the y axis is in the p1-p2-p3 plane
the x axis is the cross product of y and z.

template<class T>

numeric::HomogeneousTransform< T >::HomogeneousTransform	(	xyzVector< T > const &	xaxis,
		xyzVector< T > const &	yaxis,
		xyzVector< T > const &	zaxis,
		xyzVector< T > const &	point
	)

inline

Constructor from xyzVectors: trust that the axis are indeed orthoganol.

template<class T>

numeric::HomogeneousTransform< T >::HomogeneousTransform	(	xyzMatrix< T > const &	axes,
		xyzVector< T > const &	point
	)

inline

Constructor from an xyzMatrix and xyzVectors: trust that the axis are indeed orthoganol.

Note that variable naming scheme (e.g. xy) is oposite of that in the xyzMatrix.

Member Function Documentation

template<class T>

xyzVector< T > numeric::HomogeneousTransform< T >::euler_angles_deg ( ) const

inline

template<class T>

xyzVector< T > numeric::HomogeneousTransform< T >::euler_angles_rad ( ) const

inline

Return the three euler angles (in radians) that describe this HomogeneousTransform as the series of a Z axis rotation by the angle phi (returned in position 1 of the output vector), followed by an X axis rotation by the angle theta (returned in position 3 of the output vector), followed by another Z axis rotation by the angle psi (returned in position 2 of the output vector). This code is a modified version of Alex Z's code from r++.

The range of phi is [ -pi, pi ]; The range of psi is [ -pi, pi ]; The range of theta is [ 0, pi ];

The function pretends that this HomogeneousTransform is the result of these three transformations; if it were, then the rotation matrix would be

FIGURE 1: R = [ cos(psi)cos(phi)-cos(theta)sin(phi)sin(psi) cos(psi)sin(phi)+cos(theta)cos(phi)sin(psi) sin(psi)sin(theta) -sin(psi)cos(phi)-cos(theta)sin(phi)cos(psi) -sin(psi)sin(phi)+cos(theta)cos(phi)cos(psi) cos(psi)sin(theta) sin(theta)sin(phi) -sin(theta)cos(phi) cos(theta) ]

where each axis above is represented as a ROW VECTOR (to be distinguished from the HomogeneousTransform's representation of axes as COLUMN VECTORS).

The zz_ coordinate gives away theta. Theta may be computed as acos( zz_ ), or, as Alex does it, asin( sqrt( 1 - zz^2)) Since there is redundancy in theta, this function chooses a theta with a positive sin(theta): i.e. quadrants I and II. Assuming we have a positive sin theta pushes phi and psi into conforming angles.

NOTE on theta: asin returns a value in the range [ -pi/2, pi/2 ], and we have artificially created a positive sin(theta), so we will get a asin( pos_sin_theta ), we have a value in the range [ 0, pi/2 ]. To convert this into the actual angle theta, we examine the zz sign. If zz is negative, we chose the quadrant II theta. That is, asin( pos_sin_theta) returned an angle, call it theta'. Now, if cos( theta ) is negative, then we want to choose the positive x-axis rotation that's equivalent to -theta'. To do so, we reflect q through the y axis (See figure 2 below) to get p and then measure theta as pi - theta'.

FIGURE 2:

II | I | p. | .q (cos(-theta'), std::abs(sin(theta'))) . | .

theta'( . | . ) theta' = asin( std::abs(sin(theta))

| IV | The angle between the positive x axis and p is pi - theta'.

Since zx and zy contain only phi terms and a constant sin( theta ) term, phi is given by atan2( sin_phi, cos_phi ) = atan2( c*sin_phi, c*cos_phi ) = atan2( zx, -zy ) for c positive and non-zero. If sin_theta is zero, or very close to zero, we're at gimbal lock.

Moreover, since xz and yz contain only psi terms, psi may also be deduced using atan2.

There are 2 degenerate cases (gimbal lock)

theta close to 0 (North Pole singularity), or
theta close to pi (South Pole singularity) For these, we take: phi=acos(xx), theta = 0 (resp. Pi/2), psi = 0

Referenced by numeric::HomogeneousTransform< double >::euler_angles_deg().

template<class T>

void numeric::HomogeneousTransform< T >::from_euler_angles_deg ( xyzVector< T > const & euler )

inline

template<class T>

void numeric::HomogeneousTransform< T >::from_euler_angles_rad ( xyzVector< T > const & euler )

inline

Construct the coordinate frame from three euler angles that describe the frame. Keep the point fixed. See the description for euler_angles_rad() to understand the Z-X-Z transformation convention.

Referenced by numeric::HomogeneousTransform< double >::from_euler_angles_deg().

template<class T>

HomogeneousTransform< T > numeric::HomogeneousTransform< T >::inverse ( ) const

inline

Invert this matrix.

template<class T>

bool numeric::HomogeneousTransform< T >::normal ( ) const

inlineprivate

Are the axis of unit length?

Referenced by numeric::HomogeneousTransform< double >::orthonormal().

template<class T>

HomogeneousTransform< T > numeric::HomogeneousTransform< T >::operator* ( HomogeneousTransform< T > const & rmat ) const

inline

Multiplication.

the main operation of a homogeneous transform: matrix multiplication. Note: matrix multiplication is transitive, so rotation/translation matrices may be pre-multiplied before being applied to a set of points.

template<class T>

xyzVector< T > numeric::HomogeneousTransform< T >::operator* ( xyzVector< T > const & vect ) const

inline

Transform a point. The input point is a location in this coordinate frame the output point is the location in global coordinate frame.

template<class T>

bool numeric::HomogeneousTransform< T >::orthoganol ( ) const

inlineprivate

Are the axis orthoganol.

Referenced by numeric::HomogeneousTransform< double >::orthonormal().

template<class T>

bool numeric::HomogeneousTransform< T >::orthonormal ( ) const

inlineprivate

Referenced by numeric::HomogeneousTransform< double >::HomogeneousTransform().

template<class T>

xyzVector< T > numeric::HomogeneousTransform< T >::point ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::to_local_coordinate().

template<class T>

value_type numeric::HomogeneousTransform< T >::px ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::show().

template<class T>

value_type numeric::HomogeneousTransform< T >::py ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::show().

template<class T>

value_type numeric::HomogeneousTransform< T >::pz ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::show().

template<class T>

xyzMatrix< T > numeric::HomogeneousTransform< T >::rotation_matrix ( ) const

inline

template<class T>

void numeric::HomogeneousTransform< T >::set_identity ( )

inline

template<class T>

void numeric::HomogeneousTransform< T >::set_identity_rotation ( )

inline

Mutators.

Referenced by numeric::HomogeneousTransform< double >::set_identity(), and numeric::HomogeneousTransform< double >::set_transform().

template<class T>

void numeric::HomogeneousTransform< T >::set_identity_transform ( )

inline

Referenced by numeric::HomogeneousTransform< double >::set_identity().

template<class T>

void numeric::HomogeneousTransform< T >::set_point ( xyzVector< T > const & p )

inline

Set the point that this HT is centered at. This leaves the axes untouched.

template<class T>

void numeric::HomogeneousTransform< T >::set_transform ( xyzVector< T > const & t )

inline

Set this HT to describe a transformation along the three axes. This has the size effect of setting the axes to the global axes.

template<class T>

void numeric::HomogeneousTransform< T >::set_xaxis_rotation_deg ( T angle )

inline

template<class T>

void numeric::HomogeneousTransform< T >::set_xaxis_rotation_rad ( T angle )

inline

template<class T>

void numeric::HomogeneousTransform< T >::set_yaxis_rotation_deg ( T angle )

inline

template<class T>

void numeric::HomogeneousTransform< T >::set_yaxis_rotation_rad ( T angle )

inline

template<class T>

void numeric::HomogeneousTransform< T >::set_zaxis_rotation_deg ( T angle )

inline

template<class T>

void numeric::HomogeneousTransform< T >::set_zaxis_rotation_rad ( T angle )

inline

template<class T>

std::ostream& numeric::HomogeneousTransform< T >::show ( std::ostream & stream = std::cout ) const

inline

Referenced by pyrosetta.distributed.viewer.core.Viewer::__call__().

template<class T>

xyzVector< T > numeric::HomogeneousTransform< T >::to_local_coordinate ( xyzVector< T > const & v ) const

inline

Convert a point in the global coordinate system to a point in this coordinate frame. If this frame is F and the point is p, then this solves for x st: F x = p. Equivalent to computing (F.inverse() * p).point().

template<class T>

void numeric::HomogeneousTransform< T >::walk_along_x ( T delta )

inline

Right multiply this coordinate frame by the frame 1 0 0 delta 0 1 0 0 0 0 1 0.

template<class T>

void numeric::HomogeneousTransform< T >::walk_along_y ( T delta )

inline

Right multiply this coordinate frame by the frame 1 0 0 0 0 1 0 delta 0 0 1 0.

template<class T>

void numeric::HomogeneousTransform< T >::walk_along_z ( T delta )

inline

Right multiply this coordinate frame by the frame 1 0 0 0 0 1 0 0 0 0 1 delta.

template<class T>

xyzVector< T > numeric::HomogeneousTransform< T >::xaxis ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::HomogeneousTransform(), and numeric::HomogeneousTransform< double >::to_local_coordinate().

template<class T>

T numeric::HomogeneousTransform< T >::xform_magnitude ( T radius_of_gyration )

inline

Less accurate functions.

Used to calculate no-alignment "RMSD" of two identical poses using transforms

For this to work, the two poses must be identical, but with different orientations. Here are the steps to use this:

The radius of gyration of the pose must be calculated (see core/pose/util.hh )
There must be an archetype pose with its center of mass at the origin (this can be imaginary)
The relative transform of each of the two poses relative to the archetype must be calculated. (i.e. What transform you would apply to the archetype to move it to where the pose is.)
RMSD = ( xform1.inverse() * xform2 ).xform_magnitude( radius_of_gyration )

template<class T>

value_type numeric::HomogeneousTransform< T >::xx ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::show().

template<class T>

value_type numeric::HomogeneousTransform< T >::xy ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::show().

template<class T>

value_type numeric::HomogeneousTransform< T >::xz ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::show().

template<class T>

xyzVector< T > numeric::HomogeneousTransform< T >::yaxis ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::to_local_coordinate().

template<class T>

value_type numeric::HomogeneousTransform< T >::yx ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::show().

template<class T>

value_type numeric::HomogeneousTransform< T >::yy ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::show().

template<class T>

value_type numeric::HomogeneousTransform< T >::yz ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::show().

template<class T>

xyzVector< T > numeric::HomogeneousTransform< T >::zaxis ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::to_local_coordinate().

template<class T>

value_type numeric::HomogeneousTransform< T >::zx ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::show().

template<class T>

value_type numeric::HomogeneousTransform< T >::zy ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::show().

template<class T>

value_type numeric::HomogeneousTransform< T >::zz ( ) const

inline

Referenced by numeric::HomogeneousTransform< double >::show().

Member Data Documentation

template<class T>

value_type numeric::HomogeneousTransform< T >::px_

private

template<class T>

value_type numeric::HomogeneousTransform< T >::py_

private

template<class T>

value_type numeric::HomogeneousTransform< T >::pz_

private

template<class T>

value_type numeric::HomogeneousTransform< T >::xx_

private

For axis Q, the R component is named qr_; e.g. The Z component of the Y axis is yz_;.

Variables below are allocated in an intentionally visually pleasing order for a code reader, not necessarily for performance. The homogenous matrix is a 4 x 3 matrix, with a pseudo row-major ordering of data. Naming scheme: Column 1 is the x axis as a column vector Column 2 is the y axis as a column vector Column 3 is the z axis as a column vector Column 4 is the location of the point, as a column vector. Row 1 is the x coordinate of the three axes and the point Row 2 is the y coordinate of the three axes and the point Row 3 is the z coordinate of the three axes and the point Row 4 is not explicitly represented, but is always [ 0, 0, 0, 1 ]Note: This naming scheme is different from the one that Stuart uses in the xyzMatrix class.