Represents an homogeneous transformation in a N dimensional space
- Template Parameters:
-
| _Scalar | the scalar type, i.e., the type of the coefficients |
| _Dim | the dimension of the space |
| _Mode | the type of the transformation. Can be:
- Affine: the transformation is stored as a (Dim+1)^2 matrix, where the last row is assumed to be [0 ... 0 1].
- AffineCompact: the transformation is stored as a (Dim)x(Dim+1) matrix.
- Projective: the transformation is stored as a (Dim+1)^2 matrix without any assumption.
|
| _Options | has the same meaning as in class Matrix. It allows to specify DontAlign and/or RowMajor. These Options are passed directly to the underlying matrix type. |
The homography is internally represented and stored by a matrix which is available through the matrix() method. To understand the behavior of this class you have to think a Transform object as its internal matrix representation. The chosen convention is right multiply:
Therefore, an affine transformation matrix M is shaped like this:
Note that for a projective transformation the last row can be anything, and then the interpretation of different parts might be sightly different.
However, unlike a plain matrix, the Transform class provides many features simplifying both its assembly and usage. In particular, it can be composed with any other transformations (Transform,Translation,RotationBase,Matrix) and can be directly used to transform implicit homogeneous vectors. All these operations are handled via the operator*. For the composition of transformations, its principle consists to first convert the right/left hand sides of the product to a compatible (Dim+1)^2 matrix and then perform a pure matrix product. Of course, internally, operator* tries to perform the minimal number of operations according to the nature of each terms. Likewise, when applying the transform to non homogeneous vectors, the latters are automatically promoted to homogeneous one before doing the matrix product. The convertions to homogeneous representations are performed as follow:
Translation t (Dim)x(1): 
Rotation R (Dim)x(Dim): 
Linear Matrix L (Dim)x(Dim): 
Affine Matrix A (Dim)x(Dim+1): 
Column vector v (Dim)x(1): 
Set of column vectors V1...Vn (Dim)x(n): 
The concatenation of a Transform object with any kind of other transformation always returns a Transform object.
A little exception to the "as pure matrix product" rule is the case of the transformation of non homogeneous vectors by an affine transformation. In that case the last matrix row can be ignored, and the product returns non homogeneous vectors.
Since, for instance, a Dim x Dim matrix is interpreted as a linear transformation, it is not possible to directly transform Dim vectors stored in a Dim x Dim matrix. The solution is either to use a Dim x Dynamic matrix or explicitly request a vector transformation by making the vector homogeneous:
m' = T * m.colwise().homogeneous();
Note that there is zero overhead.
Conversion methods from/to Qt's QMatrix and QTransform are available if the preprocessor token EIGEN_QT_SUPPORT is defined.
This class can be extended with the help of the plugin mechanism described on the page TopicCustomizingEigen by defining the preprocessor symbol EIGEN_TRANSFORM_PLUGIN.
- See also:
- class Matrix, class Quaternion
Public Types |
| enum | { TransformTimeDiagonalMode = ((Mode==int(Isometry))?Affine:int(Mode))
} |
| typedef _Scalar | Scalar |
| | the scalar type of the coefficients
|
| typedef DenseIndex | Index |
typedef
internal::make_proper_matrix_type
< Scalar, Rows, HDim, Options >
::type | MatrixType |
| | type of the matrix used to represent the transformation
|
| typedef const MatrixType | ConstMatrixType |
| | constified MatrixType
|
typedef Matrix< Scalar, Dim,
Dim, Options > | LinearMatrixType |
| | type of the matrix used to represent the linear part of the transformation
|
typedef Block< MatrixType, Dim,
Dim > | LinearPart |
| | type of read/write reference to the linear part of the transformation
|
typedef const Block
< ConstMatrixType, Dim, Dim > | ConstLinearPart |
| | type of read reference to the linear part of the transformation
|
typedef internal::conditional
< int(Mode)==int(AffineCompact),
MatrixType &, Block
< MatrixType, Dim, HDim >
>::type | AffinePart |
| | type of read/write reference to the affine part of the transformation
|
typedef internal::conditional
< int(Mode)==int(AffineCompact),
const MatrixType &, const
Block< const MatrixType, Dim,
HDim > >::type | ConstAffinePart |
| | type of read reference to the affine part of the transformation
|
| typedef Matrix< Scalar, Dim, 1 > | VectorType |
| | type of a vector
|
| typedef Block< MatrixType, Dim, 1 > | TranslationPart |
| | type of a read/write reference to the translation part of the rotation
|
typedef const Block
< ConstMatrixType, Dim, 1 > | ConstTranslationPart |
| | type of a read reference to the translation part of the rotation
|
| typedef Translation< Scalar, Dim > | TranslationType |
| | corresponding translation type
|
typedef Transform< Scalar, Dim,
TransformTimeDiagonalMode > | TransformTimeDiagonalReturnType |
| | The return type of the product between a diagonal matrix and a transform.
|
typedef
internal::transform_take_affine_part
< Transform > | take_affine_part |
Public Member Functions |
| | EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE (_Scalar, _Dim==Dynamic?Dynamic:(_Dim+1)*(_Dim+1)) enum |
| | Transform () |
| | Default constructor without initialization of the meaningful coefficients.
|
| | Transform (const Transform &other) |
| | Transform (const TranslationType &t) |
| | Transform (const UniformScaling< Scalar > &s) |
| template<typename Derived > |
| | Transform (const RotationBase< Derived, Dim > &r) |
| Transform & | operator= (const Transform &other) |
| template<typename OtherDerived > |
| | Transform (const EigenBase< OtherDerived > &other) |
| | Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix.
|
| template<typename OtherDerived > |
| Transform & | operator= (const EigenBase< OtherDerived > &other) |
| | Set *this from a Dim^2 or (Dim+1)^2 matrix.
|
| template<int OtherOptions> |
| | Transform (const Transform< Scalar, Dim, Mode, OtherOptions > &other) |
| template<int OtherMode, int OtherOptions> |
| | Transform (const Transform< Scalar, Dim, OtherMode, OtherOptions > &other) |
| template<typename OtherDerived > |
| | Transform (const ReturnByValue< OtherDerived > &other) |
| template<typename OtherDerived > |
| Transform & | operator= (const ReturnByValue< OtherDerived > &other) |
| Scalar | operator() (Index row, Index col) const |
| | shortcut for m_matrix(row,col);
|
| Scalar & | operator() (Index row, Index col) |
| | shortcut for m_matrix(row,col);
|
| const MatrixType & | matrix () const |
| MatrixType & | matrix () |
| ConstLinearPart | linear () const |
| LinearPart | linear () |
| ConstAffinePart | affine () const |
| AffinePart | affine () |
| ConstTranslationPart | translation () const |
| TranslationPart | translation () |
| template<typename OtherDerived > |
EIGEN_STRONG_INLINE const
internal::transform_right_product_impl
< Transform, OtherDerived >
::ResultType | operator* (const EigenBase< OtherDerived > &other) const |
| template<typename DiagonalDerived > |
const
TransformTimeDiagonalReturnType | operator* (const DiagonalBase< DiagonalDerived > &b) const |
| template<typename OtherDerived > |
| Transform & | operator*= (const EigenBase< OtherDerived > &other) |
| const Transform | operator* (const Transform &other) const |
| | Concatenates two transformations.
|
| template<int OtherMode, int OtherOptions> |
const
internal::transform_transform_product_impl
< Transform, Transform< Scalar,
Dim, OtherMode, OtherOptions >
>::ResultType | operator* (const Transform< Scalar, Dim, OtherMode, OtherOptions > &other) const |
| | Concatenates two different transformations.
|
| void | setIdentity () |
| template<typename OtherDerived > |
| Transform & | scale (const MatrixBase< OtherDerived > &other) |
| | Applies on the right the non uniform scale transformation represented by the vector other to *this and returns a reference to *this.
|
| template<typename OtherDerived > |
| Transform & | prescale (const MatrixBase< OtherDerived > &other) |
| | Applies on the left the non uniform scale transformation represented by the vector other to *this and returns a reference to *this.
|
| Transform & | scale (Scalar s) |
| | Applies on the right a uniform scale of a factor c to *this and returns a reference to *this.
|
| Transform & | prescale (Scalar s) |
| | Applies on the left a uniform scale of a factor c to *this and returns a reference to *this.
|
| template<typename OtherDerived > |
| Transform & | translate (const MatrixBase< OtherDerived > &other) |
| | Applies on the right the translation matrix represented by the vector other to *this and returns a reference to *this.
|
| template<typename OtherDerived > |
| Transform & | pretranslate (const MatrixBase< OtherDerived > &other) |
| | Applies on the left the translation matrix represented by the vector other to *this and returns a reference to *this.
|
| template<typename RotationType > |
| Transform & | rotate (const RotationType &rotation) |
| | Applies on the right the rotation represented by the rotation rotation to *this and returns a reference to *this.
|
| template<typename RotationType > |
| Transform & | prerotate (const RotationType &rotation) |
| | Applies on the left the rotation represented by the rotation rotation to *this and returns a reference to *this.
|
| Transform & | shear (Scalar sx, Scalar sy) |
| | Applies on the right the shear transformation represented by the vector other to *this and returns a reference to *this.
|
| Transform & | preshear (Scalar sx, Scalar sy) |
| | Applies on the left the shear transformation represented by the vector other to *this and returns a reference to *this.
|
| Transform & | operator= (const TranslationType &t) |
| Transform & | operator*= (const TranslationType &t) |
| Transform | operator* (const TranslationType &t) const |
| Transform & | operator= (const UniformScaling< Scalar > &t) |
| Transform & | operator*= (const UniformScaling< Scalar > &s) |
| Transform | operator* (const UniformScaling< Scalar > &s) const |
| Transform & | operator*= (const DiagonalMatrix< Scalar, Dim > &s) |
| template<typename Derived > |
| Transform & | operator= (const RotationBase< Derived, Dim > &r) |
| template<typename Derived > |
| Transform & | operator*= (const RotationBase< Derived, Dim > &r) |
| template<typename Derived > |
| Transform | operator* (const RotationBase< Derived, Dim > &r) const |
| const LinearMatrixType | rotation () const |
| template<typename RotationMatrixType , typename ScalingMatrixType > |
| void | computeRotationScaling (RotationMatrixType *rotation, ScalingMatrixType *scaling) const |
| | decomposes the linear part of the transformation as a product rotation x scaling, the scaling being not necessarily positive.
|
| template<typename ScalingMatrixType , typename RotationMatrixType > |
| void | computeScalingRotation (ScalingMatrixType *scaling, RotationMatrixType *rotation) const |
| | decomposes the linear part of the transformation as a product rotation x scaling, the scaling being not necessarily positive.
|
| template<typename PositionDerived , typename OrientationType , typename ScaleDerived > |
| Transform & | fromPositionOrientationScale (const MatrixBase< PositionDerived > &position, const OrientationType &orientation, const MatrixBase< ScaleDerived > &scale) |
| | Convenient method to set *this from a position, orientation and scale of a 3D object.
|
| Transform | inverse (TransformTraits traits=(TransformTraits) Mode) const |
| const Scalar * | data () const |
| Scalar * | data () |
| template<typename NewScalarType > |
internal::cast_return_type
< Transform, Transform
< NewScalarType, Dim, Mode,
Options > >::type | cast () const |
| template<typename OtherScalarType > |
| | Transform (const Transform< OtherScalarType, Dim, Mode, Options > &other) |
| | Copy constructor with scalar type conversion.
|
| bool | isApprox (const Transform &other, typename NumTraits< Scalar >::Real prec=NumTraits< Scalar >::dummy_precision()) const |
| void | makeAffine () |
| | Sets the last row to [0 ...
|
Block< MatrixType, int(Mode)==int(Projective)?HDim:Dim,
Dim > | linearExt () |
const Block< MatrixType, int(Mode)==int(Projective)?HDim:Dim,
Dim > | linearExt () const |
| Block< MatrixType, int(Mode)==int(Projective)?HDim:Dim, 1 > | translationExt () |
| const Block< MatrixType, int(Mode)==int(Projective)?HDim:Dim, 1 > | translationExt () const |
Static Public Member Functions |
| static const Transform | Identity () |
| | Returns an identity transformation.
|
Protected Attributes |
| MatrixType | m_matrix |
Friends |
| template<typename OtherDerived > |
const
internal::transform_left_product_impl
< OtherDerived, Mode, Options,
_Dim, _Dim+1 >::ResultType | operator* (const EigenBase< OtherDerived > &a, const Transform &b) |
| template<typename DiagonalDerived > |
| TransformTimeDiagonalReturnType | operator* (const DiagonalBase< DiagonalDerived > &a, const Transform &b) |
