qugar::impl::AffineTransf< dim > Class Template Reference

Class for representing affine transformations. More...

#include <affine_transf.hpp>

Public Types
template<typename T >
using	Tensor = Vector<T, dim *(dim + 1) / 2>

Public Member Functions
	AffineTransf ()
	Default constructor. Creates the identity transformation.
	AffineTransf (const Point< dim > &origin)
	Constructs a new affine tranformation that simply translates the origin.
	AffineTransf (const Point< dim > &origin, real scale)
	Constructs a new affine transformation that first applies an isotropic scaling and then translates the origin.
template<int dim_aux = dim> requires (dim_aux == dim && dim == 2)
	AffineTransf (const Point< dim > &origin, const Point< dim > &axis_x)
	Constructs a new 2D affine transformation defined by an origin and the axis_x.
template<int dim_aux = dim> requires (dim_aux == dim && dim == 3)
	AffineTransf (const Point< dim > &origin, const Point< dim > &axis_x, const Point< dim > &axis_y)
	Constructs a new 3D affine transformation defined by an origin and a couple of directions that define the xy-plane.
template<int dim_aux = dim> requires (dim_aux == dim && dim == 2)
	AffineTransf (const Point< dim > &origin, const Point< dim > &axis_x, real scale_x, real scale_y)
	Constructs a new 2D affine transformation defined by an origin, the axis_x, and an orthotropic scaling along the x- and y-axes.
template<int dim_aux = dim> requires (dim_aux == dim && dim == 3)
	AffineTransf (const Point< dim > &origin, const Point< dim > &axis_x, const Point< dim > &axis_y, real scale_x, real scale_y, real scale_z)
	Constructs a new 3D affine transformation defined by an origin, a couple of directions that define the xy-plane, and an orthotropic scaling along the x-, y, and z-axes.
	AffineTransf (const Vector< real, n_coefs > &coefs)
	Constructs a new object through its coefficients. a new Affine Transf object.
AffineTransf< dim >	operator* (const AffineTransf< dim > &rhs) const
	Concatenates two affine transformation to generate a new one.
AffineTransf< dim >	inverse () const
	Inverts the current transformation.
template<typename T >
Vector< T, dim >	transform_point (const Vector< T, dim > &point) const
	Transforms a point from the original to the new reference system.
template<typename T >
Vector< T, dim >	transform_vector (const Vector< T, dim > &vector) const
	Transforms a vector from the original to the new reference system (without translation).
template<typename T >
Tensor< T >	transform_tensor (const Tensor< T > &tensor) const
	Transforms a (second-order symmetric) tensor from the original to the new reference system (without translation).

Static Public Attributes
static constexpr int	n_coefs = dim * (dim + 1)

Static Private Member Functions
static Vector< real, n_coefs >	compute_coefs (const Point< dim > &origin, real scale)
	Computes the coefficients of a new 2D affine transformation that translates the origin and apply an isotropic scaling.
template<int dim_aux = dim> requires (dim_aux == dim && dim == 3)
static Vector< real, n_coefs >	compute_coefs (const Point< dim > &origin, const Point< dim > &axis_x=Point< dim >(numbers::one, numbers::zero, numbers::zero), const Point< dim > &axis_y=Point< dim >(numbers::zero, numbers::one, numbers::zero), real scale_x=numbers::one, real scale_y=numbers::one, real scale_z=numbers::one)
	Computes the coefficients of a new 3D affine transformation defined by an origin, a couple of directions that define the xy-plane, and an orthotropic scaling along the x-, y, and z-axes.
template<int dim_aux = dim> requires (dim_aux == dim && dim == 2)
static Vector< real, n_coefs >	compute_coefs (const Point< dim > &origin, const Point< dim > &axis_x=Point< dim >(numbers::one, numbers::zero), real scale_x=numbers::one, real scale_y=numbers::one)
	Computes the coefficients of a new 2D affine transformation defined by an origin, the axis_x, and an orthotropic scaling along the x- and y-axes.

Private Attributes
Vector< real, n_coefs >	coefs_
	Transformation coefficients.

Detailed Description

template<int dim>
class qugar::impl::AffineTransf< dim >

Class for representing affine transformations.

It transforms points as y = A * x + b, where x is the original point, y is the new point, b is the translation vector, and A is the transformation matrix that may be defined by rotations and scaling.

The member coefs_ stores the involved coefficients. Thus, first dim*dim values of coefs_ contain the values of the matrix A (row-wise), and the last dim values, the ones of the vector b.

Template Parameters

dim	Parametric direction.

Member Typedef Documentation

Tensor

template<int dim>

template<typename T >

using qugar::impl::AffineTransf< dim >::Tensor = Vector<T, dim *(dim + 1) / 2>

Constructor & Destructor Documentation

AffineTransf() [1/8]

template<int dim>

qugar::impl::AffineTransf< dim >::AffineTransf ( )

explicit

Default constructor. Creates the identity transformation.

AffineTransf() [2/8]

template<int dim>

qugar::impl::AffineTransf< dim >::AffineTransf ( const Point< dim > & origin )

explicit

Constructs a new affine tranformation that simply translates the origin.

Parameters

origin

New origin of the reference system.

AffineTransf() [3/8]

template<int dim>

qugar::impl::AffineTransf< dim >::AffineTransf	(	const Point< dim > &	origin,
		real	scale )

Constructs a new affine transformation that first applies an isotropic scaling and then translates the origin.

Parameters

origin	New origin of the reference system.
scale	Scaling factor to be applied along all the directions.

AffineTransf() [4/8]

template<int dim>

template<int dim_aux = dim>
requires (dim_aux == dim && dim == 2)

qugar::impl::AffineTransf< dim >::AffineTransf	(	const Point< dim > &	origin,
		const Point< dim > &	axis_x )

Constructs a new 2D affine transformation defined by an origin and the axis_x.

It first rotates the axes and then performs the translation.

The y-axis is computed by rotating axis_x 90 degrees counter-clockwise.

Parameters

origin	New origin of the reference system.
axis_x	New x-axis of the system (it will be normalized).

AffineTransf() [5/8]

template<int dim>

template<int dim_aux = dim>
requires (dim_aux == dim && dim == 3)

qugar::impl::AffineTransf< dim >::AffineTransf	(	const Point< dim > &	origin,
		const Point< dim > &	axis_x,
		const Point< dim > &	axis_y )

Constructs a new 3D affine transformation defined by an origin and a couple of directions that define the xy-plane.

It first rotates the axes and then performs the translation.

The given axis_x and axis_y define the xy-plane, but they may not be orthonormal vectors. Thus, the way in which the new system directions are computed is as follows: First, the axis_x is normalized. Then, the z-axis is computed as the normalized cross-product of the normalized vector axis_x and axis_y. Then, the y-axis is recomputed as the cross-product between normalized vectors along the z- and the x-axes.

Parameters

origin	New origin of the reference system.
axis_x	New x-axis of the system (it will be rescaled).
axis_y	Axis defining the xy-plane together with axis_x. It must be not parallel to axis_x.

AffineTransf() [6/8]

template<int dim>

template<int dim_aux = dim>
requires (dim_aux == dim && dim == 2)

qugar::impl::AffineTransf< dim >::AffineTransf	(	const Point< dim > &	origin,
		const Point< dim > &	axis_x,
		real	scale_x,
		real	scale_y )

Constructs a new 2D affine transformation defined by an origin, the axis_x, and an orthotropic scaling along the x- and y-axes.

It first applies the scaling, then rotates the axes, and finally performs the translation.

The y-axis is computed by rotating axis_x 90 degrees counter-clockwise.

Parameters

origin	New origin of the reference system.
axis_x	New x-axis of the system (it will be rescaled).
scale_x	Scaling along the new x-axis.
scale_y	Scaling along the new y-axis.

AffineTransf() [7/8]

template<int dim>

template<int dim_aux = dim>
requires (dim_aux == dim && dim == 3)

qugar::impl::AffineTransf< dim >::AffineTransf	(	const Point< dim > &	origin,
		const Point< dim > &	axis_x,
		const Point< dim > &	axis_y,
		real	scale_x,
		real	scale_y,
		real	scale_z )

Constructs a new 3D affine transformation defined by an origin, a couple of directions that define the xy-plane, and an orthotropic scaling along the x-, y, and z-axes.

It first applies the scaling, then rotates the axes, and finally performs the translation.

The given axis_x and axis_y define the xy-plane, but they may not be orthonormal vectors. Thus, the way in which the new system directions are computed is as follows: First, the axis_x is normalized. Then, the z-axis is computed as the normalized cross-product of the normalized vector axis_x and axis_y. Then, the y-axis is recomputed as the cross-product between normalized vectors along the z- and the x-axes.

Parameters

origin	New origin of the reference system.
axis_x	New x-axis of the system (it will be rescaled).
axis_y	Axis defining the xy-plane together with axis_x. It must be not parallel to axis_x.
scale_x	Scaling along the new x-axis.
scale_y	Scaling along the new y-axis.
scale_z	Scaling along the new z-axis.

AffineTransf() [8/8]

template<int dim>

qugar::impl::AffineTransf< dim >::AffineTransf ( const Vector< real, n_coefs > & coefs )

explicit

Constructs a new object through its coefficients. a new Affine Transf object.

See the class documentation for information about the coefficients.

Parameters

coefs

Transformation coefficients.

Member Function Documentation

compute_coefs() [1/3]

template<int dim>

template<int dim_aux = dim>
requires (dim_aux == dim && dim == 2)

static Vector< real, n_coefs > qugar::impl::AffineTransf< dim >::compute_coefs ( const Point< dim > & origin, const Point< dim > & axis_x = Point< dim >(numbers::one, numbers::zero), real scale_x = numbers::one, real scale_y = numbers::one )

staticnodiscardprivate

Computes the coefficients of a new 2D affine transformation defined by an origin, the axis_x, and an orthotropic scaling along the x- and y-axes.

It first applies the scaling, then rotates the axes, and finally performs the translation.

The y-axis is computed by rotating axis_x 90 degrees counter-clockwise.

The scaling is performed respect to the new (rotated/translated) reference system.

Parameters

origin	New origin of the reference system.
axis_x	New x-axis of the system (it will be rescaled).
scale_x	Scaling along the new x-axis.
scale_y	Scaling along the new y-axis.

compute_coefs() [2/3]

template<int dim>

template<int dim_aux = dim>
requires (dim_aux == dim && dim == 3)

static Vector< real, n_coefs > qugar::impl::AffineTransf< dim >::compute_coefs ( const Point< dim > & origin, const Point< dim > & axis_x = Point< dim >(numbers::one, numbers::zero, numbers::zero), const Point< dim > & axis_y = Point< dim >(numbers::zero, numbers::one, numbers::zero), real scale_x = numbers::one, real scale_y = numbers::one, real scale_z = numbers::one )

staticnodiscardprivate

Computes the coefficients of a new 3D affine transformation defined by an origin, a couple of directions that define the xy-plane, and an orthotropic scaling along the x-, y, and z-axes.

It first applies the scaling, then rotates the axes, and finally performs the translation.

The given axis_x and axis_y define the xy-plane, but they may not be orthonormal vectors. Thus, the way in which the new system directions are computed is as follows: First, the axis_x is normalized. Then, the z-axis is computed as the normalized cross-product of the normalized vector axis_x and axis_y. Then, the y-axis is recomputed as the cross-product between normalized vectors along the z- and the x-axes.

The scaling is performed respect to the new (rotated/translated) reference system.

Parameters

origin	New origin of the reference system.
axis_x	New x-axis of the system (it will be rescaled).
axis_y	Axis defining the xy-plane together with axis_x. It must be not parallel to axis_x.
scale_x	Scaling along the new x-axis.
scale_y	Scaling along the new y-axis.
scale_z	Scaling along the new z-axis.

Returns

Computed coefficients.

compute_coefs() [3/3]

template<int dim>

static Vector< real, n_coefs > qugar::impl::AffineTransf< dim >::compute_coefs ( const Point< dim > & origin, real scale )

staticnodiscardprivate

Computes the coefficients of a new 2D affine transformation that translates the origin and apply an isotropic scaling.

It first applies the scaling and then performs the translation.

Parameters

origin	New origin of the reference system.
scale	Scaling factor to be applied along all the directions.

Returns

Computed coefficients.

inverse()

template<int dim>

AffineTransf< dim > qugar::impl::AffineTransf< dim >::inverse

(

)

const

Inverts the current transformation.

Returns

Inverted transformation.

operator*()

template<int dim>

AffineTransf< dim > qugar::impl::AffineTransf< dim >::operator*

(

const AffineTransf< dim > &

rhs

)

const

Concatenates two affine transformation to generate a new one.

The new generated transformation is equivalent to, first, applying the given rhs transformation to a point (gradient, hessian), and then, the current one.

Parameters

rhs	First transformation to apply.

Returns

Concatenated transformations.

transform_point()

template<int dim>

template<typename T >

Vector< T, dim > qugar::impl::AffineTransf< dim >::transform_point ( const Vector< T, dim > & point ) const

nodiscard

Transforms a point from the original to the new reference system.

Template Parameters

T	Type of the point.

Parameters

point

Point to be transformed.

Returns

Transformed point.

transform_tensor()

template<int dim>

template<typename T >

Tensor< T > qugar::impl::AffineTransf< dim >::transform_tensor ( const Tensor< T > & tensor ) const

nodiscard

Transforms a (second-order symmetric) tensor from the original to the new reference system (without translation).

Template Parameters

T	Type of the tensor.

Parameters

tensor

Second-order symmetric tensor to be transformed.

Returns

Transformed tnesor.

transform_vector()

template<int dim>

template<typename T >

Vector< T, dim > qugar::impl::AffineTransf< dim >::transform_vector ( const Vector< T, dim > & vector ) const

nodiscard

Transforms a vector from the original to the new reference system (without translation).

Template Parameters

T	Type of the vector.

Parameters

vector

Vector to be transformed.

Returns

Transformed vector.

Member Data Documentation

coefs_

template<int dim>

Vector<real, n_coefs> qugar::impl::AffineTransf< dim >::coefs_

private

Transformation coefficients.

n_coefs

template<int dim>

int qugar::impl::AffineTransf< dim >::n_coefs = dim * (dim + 1)

staticconstexpr

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The documentation for this class was generated from the following file:

• /__w/qugar/qugar/cpp/include/qugar/affine_transf.hpp