Transforms

struct InvalidEulerAxesException : public exception: Exception thrown when using an invalid Euler axes order, e.g., when providing an invalid uint8_t.

struct InvalidTransformException : public motion3d::MessageException: Exception thrown when performing operations including non-unsafe and invalid transforms.

struct InvalidTransformTypeException : public exception: Exception thrown when using an invalid transform type, e.g., when providing an invalid char.

struct InvalidTypeSizeException : public exception: Exception thrown when a transform is created from binary or vector data of the wrong size.

enum class motion3d::EulerAxes : std::uint8_t

Enumerate of all available Euler axes orders.

Values:

enumerator kSXYZ

enumerator kSXYX

enumerator kSXZY

enumerator kSXZX

enumerator kSYZX

enumerator kSYZY

enumerator kSYXZ

enumerator kSYXY

enumerator kSZXY

enumerator kSZXZ

enumerator kSZYX

enumerator kSZYZ

enumerator kRZYX

enumerator kRXYX

enumerator kRYZX

enumerator kRXZX

enumerator kRXZY

enumerator kRYZY

enumerator kRZXY

enumerator kRYXY

enumerator kRYXZ

enumerator kRZXZ

enumerator kRXYZ

enumerator kRZYZ

enum class motion3d::TransformType

Transformation representation type.

Values:

enumerator kAxisAngle

enumerator kDualQuaternion

enumerator kEuler

enumerator kMatrix

enumerator kQuaternion

class TransformInterface

Interface class for generic access to transformations.

Subclassed by motion3d::TransformBase< Derived >, motion3d::TransformBase< AxisAngleTransform >, motion3d::TransformBase< DualQuaternionTransform >, motion3d::TransformBase< EulerTransform >, motion3d::TransformBase< MatrixTransform >, motion3d::TransformBase< QuaternionTransform >

Public Functions

DEFINE_POINTERS(TransformInterface)

virtual ~TransformInterface() = default

inline TransformInterface::Ptr copy() const: Constructs and initializes a copy of *this.

inline TransformInterface::Ptr setIdentity(): Set *this to an identity transform.

inline TransformInterface::Ptr identity() const: Constructs and initializes an identity transform with the same type as *this.

virtual TransformType getType() const = 0

Returns:: the transform type of *this.

virtual bool isType(const TransformType &type) const = 0

Returns:: if the transform type of *this is type.

virtual TransformInterface::Ptr asType(const TransformType &type) const = 0: Converts *this to transform type type.

template<typename T> std::shared_ptr<T> asType() const: Converts *this to transform type T.

inline TransformInterface::Ptr inverse_(): Inplace variant of inverse().

inline TransformInterface::Ptr inverse() const

Returns:: the inverse transform to *this.

inline TransformInterface::Ptr normalized_(): Inplace variant of normalized().

inline TransformInterface::Ptr normalized() const: Normalizes *this to a valid transform and sets unsafe to false.

inline TransformInterface::Ptr scaleTranslation_(double factor): Inplace variant of scaleTranslation().

inline TransformInterface::Ptr scaleTranslation(double factor) const: Scales the translation by factor.

inline virtual TransformInterface::Ptr applyPre_(const TransformInterface::ConstPtr &other): Inplace variant of applyPre(const TransformInterface::ConstPtr&).

inline virtual TransformInterface::Ptr applyPre(const TransformInterface::ConstPtr &other) const

Applies other transform $T_\mathrm{o}$ before *this transform $T$ :

$T_\mathrm{o} \circ T$

inline virtual TransformInterface::Ptr applyPost_(const TransformInterface::ConstPtr &other): Inplace variant of applyPost(const TransformInterface::ConstPtr&).

inline virtual TransformInterface::Ptr applyPost(const TransformInterface::ConstPtr &other) const

Applies other transform $T_\mathrm{o}$ after *this transform $T$ :

$T \circ T_\mathrm{o}$

virtual TransformInterface::Ptr applyPre_(const TransformInterface &other) = 0: Inplace variant of applyPre(const TransformInterface&).

virtual TransformInterface::Ptr applyPre(const TransformInterface &other) const = 0

virtual Eigen::Matrix<double, 3, 1> transformPoint(const Eigen::Ref<const Eigen::Matrix<double, 3, 1>> &point) const = 0: Applies *this on 3D point.

virtual Eigen::Matrix<double, 3, Eigen::Dynamic> transformCloud(const Eigen::Ref<const Eigen::Matrix<double, 3, Eigen::Dynamic>> &cloud) const = 0: Applies *this on 3D point cloud.

virtual std::vector<std::uint8_t> toBinary() const = 0: Converts *this to a binary vector.

virtual std::vector<double> toVector() const = 0: Converts *this to an std vector.

virtual Eigen::Matrix<double, Eigen::Dynamic, 1> toEigenVector() const = 0: Converts *this to an Eigen vector.

virtual bool isUnsafe() const = 0

Returns:: if *this is marked unsafe, meaning that the validity check is skipped at each operation.

virtual bool isValid() const = 0

Returns:: if *this is valid using a default eps for isValid(double) const.

virtual bool isValid(double eps) const = 0

Returns:: if *this is valid w.r.t the threshold eps.

virtual bool isEqual(const TransformInterface::ConstPtr &other) const = 0

Returns:: if *this is equal to other using a default eps for isEqual(const TransformInterface::ConstPtr&, double) const.

virtual bool isEqual(const TransformInterface::ConstPtr &other, double eps) const = 0

Returns:: if *this is equal to other w.r.t the threshold eps.

virtual double rotationNorm() const = 0

Returns:: the rotation norm in rad.

virtual double translationNorm() const = 0

Returns:: the translation norm.

virtual std::string desc() const = 0

Returns:: a description of *this.

virtual std::ostream &stream(std::ostream &os) const = 0: Inserts a description of *this.

Public Static Functions

template<typename ...Args> static TransformInterface::Ptr Factory(const TransformType &type, Args&&... args)

Constructs and initializes a transform of TransformType type.

Throws:: InvalidTypeSizeException – for an invalid vector size.

Private Functions

virtual TransformInterface::Ptr copyImpl() const = 0

virtual TransformInterface::Ptr setIdentityImpl() = 0

virtual TransformInterface::Ptr identityImpl() const = 0

virtual TransformInterface::Ptr inverseImpl_() = 0

virtual TransformInterface::Ptr inverseImpl() const = 0

virtual TransformInterface::Ptr normalizedImpl_() = 0

virtual TransformInterface::Ptr normalizedImpl() const = 0

virtual TransformInterface::Ptr scaleTranslationImpl_(double factor) = 0

virtual TransformInterface::Ptr scaleTranslationImpl(double factor) const = 0

virtual TransformInterface::Ptr applyPreImpl_(const TransformInterface::ConstPtr &other) = 0

virtual TransformInterface::Ptr applyPreImpl(const TransformInterface::ConstPtr &other) const = 0

virtual TransformInterface::Ptr applyPostImpl_(const TransformInterface::ConstPtr &other) = 0

virtual TransformInterface::Ptr applyPostImpl(const TransformInterface::ConstPtr &other) const = 0

class AxisAngleTransform : public motion3d::TransformBase<AxisAngleTransform>

Axis-angle transformation consisting of a translation vector, a rotation axis and a rotation angle around this axis.

For representing a valid spatial transformation, the rotation axis must have unit length. An unsafe transform means that the validity check, usually performed at each operation, is skipped.

Public Functions

DEFINE_POINTERS(AxisAngleTransform)

AxisAngleTransform(): Constructs and initializes an AxisAngleTransform as identity transform.

template<typename Derived> AxisAngleTransform(const Eigen::DenseBase<Derived> &translation, Eigen::AngleAxis<double> angle_axis, bool unsafe = false): Constructs and initializes an AxisAngleTransform from translation vector and axis-angle rotation angle_axis.

template<typename DerivedTrans, typename DerivedAxis> AxisAngleTransform(const Eigen::DenseBase<DerivedTrans> &translation, double angle, const Eigen::MatrixBase<DerivedAxis> &axis, bool unsafe = false): Constructs and initializes an AxisAngleTransform from translation vector, rotation angle in rad, and rotation axis.

explicit AxisAngleTransform(const std::vector<std::uint8_t> &binary, bool unsafe = false)

Constructs and initializes an AxisAngleTransform from binary data.

Throws:: InvalidTypeSizeException – for an invalid binary size.

explicit AxisAngleTransform(const std::vector<double> &vector, bool unsafe = false)

Constructs and initializes an AxisAngleTransform from vector data.

Throws:: InvalidTypeSizeException – for an invalid vector size.

template<typename Derived> explicit AxisAngleTransform(const Eigen::DenseBase<Derived> &matrix, bool unsafe = false)

Constructs and initializes an AxisAngleTransform from an Eigen vector matrix.

Throws:: InvalidTypeSizeException – for an invalid matrix size.

inline AxisAngleTransform copy() const: Create a copy of *this.

AxisAngleTransform &setIdentity(): Set *this to an identity transform.

virtual std::vector<double> toVector() const override: Converts *this to an std vector.

virtual Eigen::Matrix<double, Eigen::Dynamic, 1> toEigenVector() const override: Converts *this to an Eigen vector.

template<class T> T asType() const: Converts *this to transform type T.

virtual bool isValid(double eps) const override

Checks if *this is valid w.r.t.

the threshold eps.

AxisAngleTransform &inverse_(): Inplace variant of inverse().

AxisAngleTransform inverse() const

Returns:: the inverse transform to *this.

AxisAngleTransform &normalized_(): Inplace variant of normalized().

AxisAngleTransform normalized() const: Normalizes *this to a valid axis-angle transform and sets unsafe to false.

AxisAngleTransform &scaleTranslation_(double factor): Inplace variant of scaleTranslation().

AxisAngleTransform scaleTranslation(double factor) const: Scales the translation by factor.

template<class T> AxisAngleTransform &applyPre_(const T &other): Inplace variant of applyPre().

template<class T> AxisAngleTransform applyPre(const T &other) const

Applies other transform $T_\mathrm{o}$ before *this transform $T$ :

$T_\mathrm{o} \circ T$

template<class T> AxisAngleTransform &applyPost_(const T &other): Inplace variant of applyPost().

template<class T> AxisAngleTransform applyPost(const T &other) const

Applies other transform $T_\mathrm{o}$ after *this transform $T$ :

$T \circ T_\mathrm{o}$

template<typename Derived> Eigen::Matrix<double, 3, 1> transformPoint(const Eigen::MatrixBase<Derived> &point) const: Applies *this on 3D point.

template<typename Derived> Eigen::Matrix<double, 3, Derived::ColsAtCompileTime> transformCloud(const Eigen::MatrixBase<Derived> &cloud) const: Applies *this on 3D point cloud.

virtual double rotationNorm() const override

Returns:: the rotation norm in rad.

virtual double translationNorm() const override

Returns:: the translation norm.

inline const Eigen::Matrix<double, 3, 1> &getTranslation() const

Returns:: the translation vector.

inline const Eigen::AngleAxis<double> &getAngleAxis() const

Returns:: the angle-axis rotation.

inline double getAngle() const

Returns:: the rotation angle in rad.

inline const Eigen::Matrix<double, 3, 1> &getAxis() const

Returns:: the rotation axis.

template<typename Derived> AxisAngleTransform &setTranslation(const Eigen::MatrixBase<Derived> &translation, bool unsafe = false): Sets the translation vector.

AxisAngleTransform &setAngleAxis(const Eigen::AngleAxis<double> &angle_axis, bool unsafe = false): Sets the angle-axis rotation.

AxisAngleTransform &setAngle(const double &angle, bool unsafe = false): Sets the rotation angle in rad.

template<typename Derived> AxisAngleTransform &setAxis(const Eigen::MatrixBase<Derived> &axis, bool unsafe = false): Sets the rotation axis.

inline virtual std::string desc() const override

Returns:: a description of *this.

virtual std::ostream &stream(std::ostream &os) const override: Inserts a description of *this.

template<class T> AxisAngleTransform &operator*=(const T &other): Applies other after *this.

template<class T> AxisAngleTransform &operator/=(const T &other): Applies the inverse of other after *this.

Public Static Functions

template<typename Derived> static bool isUnitAxis(const Eigen::MatrixBase<Derived> &axis, double eps)

Checks if axis is unit w.r.t.

the threshold eps.

Private Members

Eigen::Matrix<double, 3, 1> translation_: Translation vector.

Eigen::AngleAxis<double> angle_axis_: Angle-axis rotation.

class DualQuaternionTransform : public motion3d::TransformBase<DualQuaternionTransform>

Transformation consisting of a unit DualQuaternion $\mathcal{Q}=\mathrm{r} + \epsilon \, \mathrm{d}$ .

For representing a valid spatial transformation, the dual quaternion must be unit, i.e., $||\mathrm{r}|| = 1$ and $\mathrm{r}^{\ast} \, \mathrm{d} + \mathrm{d}^{\ast} \, \mathrm{r} = 0$ . An unsafe transform means that the validity check, usually performed at each operation, is skipped.

Operations:

Concatenation: $\mathcal{Q}_{ac} = \mathcal{Q}_{ab} \mathcal{Q}_{bc}$
Inversion: $V^{-1} \equiv \mathcal{Q}^{\ast}$
Point transformation: $(1 + \epsilon \, \{ 0, \boldsymbol{p}_a \} ) = \mathcal{Q}_{ab} ( 1 + \epsilon \, \{ 0, \boldsymbol{p}_b \} ) \ \bar{\mathcal{Q}}_{ab}^{*}$

Public Functions

DEFINE_POINTERS(DualQuaternionTransform)

DualQuaternionTransform(): Constructs and initializes a DualQuaternionTransform as identity transform.

explicit DualQuaternionTransform(DualQuaternion<double> dq, bool unsafe = false): Constructs and initializes a DualQuaternionTransform from dual quaternion dq.

DualQuaternionTransform(const Quaternion<double> &real, const Quaternion<double> &dual, bool unsafe = false): Constructs and initializes a DualQuaternionTransform from real and dual part.

template<typename DerivedReal, typename DerivedDual> DualQuaternionTransform(const Eigen::DenseBase<DerivedReal> &real, const Eigen::DenseBase<DerivedDual> &dual, bool unsafe = false): Constructs and initializes a DualQuaternionTransform from real and dual part Eigen matrices.

explicit DualQuaternionTransform(const std::vector<std::uint8_t> &binary, bool unsafe = false)

Constructs and initializes a DualQuaternionTransform from binary data.

Throws:: InvalidTypeSizeException – for an invalid binary size.

explicit DualQuaternionTransform(const std::vector<double> &vector, bool unsafe = false)

Constructs and initializes a DualQuaternionTransform from vector data.

Throws:: InvalidTypeSizeException – for an invalid vector size.

template<typename Derived> explicit DualQuaternionTransform(const Eigen::DenseBase<Derived> &matrix, bool unsafe = false)

Constructs and initializes a DualQuaternionTransform from an Eigen vector matrix.

Throws:: InvalidTypeSizeException – for an invalid matrix size.

inline DualQuaternionTransform copy() const: Create a copy of *this.

DualQuaternionTransform &setIdentity(): Set *this to an identity transform.

virtual std::vector<double> toVector() const override: Converts *this to an std vector.

virtual Eigen::Matrix<double, Eigen::Dynamic, 1> toEigenVector() const override: Converts *this to an Eigen vector.

template<class T> T asType() const: Converts *this to transform type T.

virtual bool isValid(double eps) const override

Checks if *this is valid w.r.t.

the threshold eps.

DualQuaternionTransform &inverse_(): Inplace variant of inverse().

DualQuaternionTransform inverse() const

Returns:: the inverse transform to *this.

DualQuaternionTransform &normalized_(): Inplace variant of normalized().

DualQuaternionTransform normalized() const: Normalizes *this to a valid dual quaternion transform and sets unsafe to false.

DualQuaternionTransform &scaleTranslation_(double factor): Inplace variant of scaleTranslation().

DualQuaternionTransform scaleTranslation(double factor) const: Scales the translation by factor.

template<class T> DualQuaternionTransform &applyPre_(const T &other): Inplace variant of applyPre().

template<class T> DualQuaternionTransform applyPre(const T &other) const

Applies other transform $T_\mathrm{o}$ before *this transform $T$ :

$T_\mathrm{o} \circ T$

template<class T> DualQuaternionTransform &applyPost_(const T &other): Inplace variant of applyPost().

template<class T> DualQuaternionTransform applyPost(const T &other) const

Applies other transform $T_\mathrm{o}$ after *this transform $T$ :

$T \circ T_\mathrm{o}$

template<typename Derived> Eigen::Matrix<double, 3, 1> transformPoint(const Eigen::MatrixBase<Derived> &point) const: Applies *this on 3D point.

template<typename Derived> Eigen::Matrix<double, 3, Derived::ColsAtCompileTime> transformCloud(const Eigen::MatrixBase<Derived> &cloud) const: Applies *this on 3D point cloud.

virtual double rotationNorm() const override

Returns:: the rotation norm in rad.

virtual double translationNorm() const override

Returns:: the translation norm.

inline const DualQuaternion<double> &getDualQuaternion() const

Returns:: the dual quaternion.

inline const Quaternion<double> &getReal() const

Returns:: the real part.

inline const Quaternion<double> &getDual() const

Returns:: the dual part.

DualQuaternionTransform &setDualQuaternion(const DualQuaternion<double> &dq, bool unsafe = false): Sets the dual quaternion.

DualQuaternionTransform &setReal(const Quaternion<double> &real, bool unsafe = false): Sets the real part.

DualQuaternionTransform &setDual(const Quaternion<double> &dual, bool unsafe = false): Sets the dual part.

inline virtual std::string desc() const override

Returns:: a description of *this.

virtual std::ostream &stream(std::ostream &os) const override: Inserts a description of *this.

template<class T> DualQuaternionTransform &operator*=(const T &other): Applies other after *this.

template<class T> DualQuaternionTransform &operator/=(const T &other): Applies the inverse of other after *this.

Public Static Functions

static bool isUnitDualQuaternion(const Quaternion<double> &real, const Quaternion<double> &dual, double eps)

Checks if dual quaternion with real and dual parts is unit w.r.t.

the threshold eps.

Private Members

DualQuaternion<double> dq_: Dual quaternion.

class EulerTransform : public motion3d::TransformBase<EulerTransform>

Euler transformation consisting of a translation vector and Euler rotation angles around three axes in a configurable order.

All possible orders are defined in the motion3d::EulerAxes enumerate. Since the Euler angles are not subject to any constraints, they are always valid.

Public Functions

DEFINE_POINTERS(EulerTransform)

EulerTransform(): Constructs and initializes an EulerTransform as identity transform.

EulerTransform(const AxisAngleTransform &obj, EulerAxes axes): Constructs and initializes an EulerTransform from AxisAngleTransform obj with specific Euler axes order.

EulerTransform(const DualQuaternionTransform &obj, EulerAxes axes): Constructs and initializes an EulerTransform from DualQuaternionTransform obj with specific Euler axes order.

EulerTransform(const EulerTransform &obj, EulerAxes axes): Constructs and initializes an EulerTransform from EulerTransform obj with specific Euler axes order.

EulerTransform(const MatrixTransform &obj, EulerAxes axes): Constructs and initializes an EulerTransform from MatrixTransform obj with specific Euler axes order.

EulerTransform(const QuaternionTransform &obj, EulerAxes axes): Constructs and initializes an EulerTransform from QuaternionTransform obj with specific Euler axes order.

template<typename Derived> EulerTransform(const Eigen::DenseBase<Derived> &translation, double ai, double aj, double ak, EulerAxes axes = kEulerAxesDefault, bool unsafe = false): Constructs and initializes an EulerTransform from a translation vector, separate rotation angles in rad, and Euler axes order.

template<typename DerivedTrans, typename DerivedAngles> EulerTransform(const Eigen::DenseBase<DerivedTrans> &translation, const Eigen::DenseBase<DerivedAngles> &angles, EulerAxes axes = kEulerAxesDefault, bool unsafe = false): Constructs and initializes an EulerTransform from a translation vector, rotation angles in rad, and Euler axes order.

explicit EulerTransform(const std::vector<std::uint8_t> &binary, bool unsafe = false)

Constructs and initializes an EulerTransform from binary data.

Throws:: InvalidTypeSizeException – for an invalid binary size.

explicit EulerTransform(const std::vector<double> &vector, bool unsafe = false)

Constructs and initializes an EulerTransform from vector data.

Throws:: InvalidTypeSizeException – for an invalid vector size.

template<typename Derived> explicit EulerTransform(const Eigen::DenseBase<Derived> &matrix, bool unsafe = false)

Constructs and initializes an EulerTransform from an Eigen vector matrix.

Throws:: InvalidTypeSizeException – for an invalid matrix size.

inline EulerTransform copy() const: Create a copy of *this.

EulerTransform &setIdentity(): Set *this to an identity transform.

virtual std::vector<double> toVector() const override: Converts *this to an std vector.

virtual Eigen::Matrix<double, Eigen::Dynamic, 1> toEigenVector() const override: Converts *this to an Eigen vector.

template<class T> T asType() const: Converts *this to transform type T.

virtual bool isValid(double eps) const override

Checks if *this is valid w.r.t.

the threshold eps.

EulerTransform &changeAxes_(EulerAxes axes): Inplace variant of changeAxes().

EulerTransform changeAxes(EulerAxes axes) const: Change Euler axes order.

EulerTransform &inverse_(): Inplace variant of inverse().

EulerTransform inverse() const

Returns:: the inverse transform to *this.

EulerTransform &normalized_(): Inplace variant of normalized().

EulerTransform normalized() const: Normalizes *this to a valid Euler transform and sets unsafe to false.

EulerTransform &scaleTranslation_(double factor): Inplace variant of scaleTranslation().

EulerTransform scaleTranslation(double factor) const: Scales the translation by factor.

template<class T> EulerTransform &applyPre_(const T &other): Inplace variant of applyPre().

template<class T> EulerTransform applyPre(const T &other) const

Applies other transform $T_\mathrm{o}$ before *this transform $T$ :

$T_\mathrm{o} \circ T$

template<class T> EulerTransform &applyPost_(const T &other): Inplace variant of applyPost().

template<class T> EulerTransform applyPost(const T &other) const

Applies other transform $T_\mathrm{o}$ after *this transform $T$ :

$T \circ T_\mathrm{o}$

template<typename Derived> Eigen::Matrix<double, 3, 1> transformPoint(const Eigen::MatrixBase<Derived> &point) const: Applies *this on 3D point.

template<typename Derived> Eigen::Matrix<double, 3, Derived::ColsAtCompileTime> transformCloud(const Eigen::MatrixBase<Derived> &cloud) const: Applies *this on 3D point cloud.

virtual double rotationNorm() const override

Returns:: the rotation norm in rad.

virtual double translationNorm() const override

Returns:: the translation norm.

inline const Eigen::Matrix<double, 3, 1> &getTranslation() const

Returns:: the translation vector.

inline double getAi() const

Returns:: the rotation around axis $i$ in rad.

inline double getAj() const

Returns:: the rotation around axis $j$ in rad.

inline double getAk() const

Returns:: the rotation around axis $k$ in rad.

Eigen::Matrix<double, 3, 1> getAngles() const

Returns:: the rotations around all axes in order $[i \ j \ k]$ in rad as Eigen matrix.

inline EulerAxes getAxes() const

Returns:: the Euler axes order.

template<typename Derived> EulerTransform &setTranslation(const Eigen::MatrixBase<Derived> &translation, bool unsafe = false): Sets the translation vector.

EulerTransform &setAi(const double &ai, bool unsafe = false): Sets the rotation around axis $i$ in rad.

EulerTransform &setAj(const double &aj, bool unsafe = false): Sets the rotation around axis $j$ in rad.

EulerTransform &setAk(const double &ak, bool unsafe = false): Sets the rotation around axis $k$ in rad.

template<typename Derived> EulerTransform &setAngles(const Eigen::MatrixBase<Derived> &angles, bool unsafe = false): Sets the rotations around all axes in order $[i \ j \ k]$ in rad as Eigen matrix.

EulerTransform &setAxes(const EulerAxes &axes, bool unsafe = false): Sets the Euler axes order.

inline virtual std::string desc() const override

Returns:: a description of *this.

virtual std::ostream &stream(std::ostream &os) const override: Inserts a description of *this.

template<class T> EulerTransform &operator*=(const T &other): Applies other after *this.

template<class T> EulerTransform &operator/=(const T &other): Applies the inverse of other after *this.

Private Members

Eigen::Matrix<double, 3, 1> translation_: Translation vector.

double ai_: Rotation around axis $i$ in rad

double aj_: Rotation around axis $j$ in rad

double ak_: Rotation around axis $k$ in rad

EulerAxes axes_: Euler axes order.

class MatrixTransform : public motion3d::TransformBase<MatrixTransform>

Matrix transformation consisting of a homogeneous $\mathrm{SE(3)}$ transformation matrix.

The matrix

$\quad \boldsymbol{M} = \begin{bmatrix} \boldsymbol{R} & \boldsymbol{t} \\ \boldsymbol{0} & 1 \end{bmatrix}$

consists of the 3x3 rotation matrix $\boldsymbol{R} \in \mathrm{SO(3)}$ and the translation vector $\boldsymbol{t}$ .

For representing a valid spatial transformation, the rotation matrix must be orthogonal and have determinant +1. An unsafe transform means that the validity check, usually performed at each operation, is skipped.

Operations:

Concatenation: $\mathrm{M}_{ac} = \mathrm{M}_{ab} \mathrm{M}_{bc}$
Inversion: $V^{-1} \equiv \begin{bmatrix} \boldsymbol{R}^\mathrm{T} & - \boldsymbol{R}^\mathrm{T} \boldsymbol{t} \\ \boldsymbol{0} & 1 \end{bmatrix}$
Point transformation: $[\boldsymbol{p}_a \ 1]^\mathrm{T} = \mathrm{M}_{ab} \, [\boldsymbol{p}_b \ 1]^\mathrm{T}$

Public Functions

DEFINE_POINTERS(MatrixTransform)

MatrixTransform(): Constructs and initializes a MatrixTransform as identity transform.

MatrixTransform(const Eigen::Matrix<double, 3, 1> &translation, const Eigen::Matrix<double, 3, 3> &rotation_matrix, bool unsafe = false): Constructs and initializes a MatrixTransform from a translation vector and a $\mathrm{SO(3)}$ rotation_matrix.

explicit MatrixTransform(const std::vector<std::uint8_t> &binary, bool unsafe = false)

Constructs and initializes a MatrixTransform from binary data.

Throws:: InvalidTypeSizeException – for an invalid binary size.

explicit MatrixTransform(const std::vector<double> &vector, bool unsafe = false)

Constructs and initializes a MatrixTransform from vector data.

Throws:: InvalidTypeSizeException – for an invalid vector size.

template<typename Derived> explicit MatrixTransform(const Eigen::DenseBase<Derived> &matrix, bool unsafe = false)

Constructs and initializes a MatrixTransform from.

a homogeneous $\mathrm{SE(3)}$ transformation matrix.
the upper 3x4 part of a homogeneous $\mathrm{SE(3)}$ transformation matrix.
an Eigen vector matrix.

Throws:: InvalidTypeSizeException – for an invalid size.

inline MatrixTransform copy() const: Create a copy of *this.

MatrixTransform &setIdentity(): Set *this to an identity transform.

virtual std::vector<double> toVector() const override: Converts *this to an std vector.

virtual Eigen::Matrix<double, Eigen::Dynamic, 1> toEigenVector() const override: Converts *this to an Eigen vector.

template<class T> T asType() const: Converts *this to transform type T.

virtual bool isValid(double eps) const override

Checks if *this is valid w.r.t.

the threshold eps.

MatrixTransform &inverse_(): Inplace variant of inverse().

MatrixTransform inverse() const

Returns:: the inverse transform to *this.

MatrixTransform &normalized_(): Inplace variant of normalized().

MatrixTransform normalized() const: Normalizes *this to a valid matrix transform and sets unsafe to false.

MatrixTransform &scaleTranslation_(double factor): Inplace variant of scaleTranslation().

MatrixTransform scaleTranslation(double factor) const: Scales the translation by factor.

template<class T> MatrixTransform &applyPre_(const T &other): Inplace variant of applyPre().

template<class T> MatrixTransform applyPre(const T &other) const

Applies other transform $T_\mathrm{o}$ before *this transform $T$ :

$T_\mathrm{o} \circ T$

template<class T> MatrixTransform &applyPost_(const T &other): Inplace variant of applyPost().

template<class T> MatrixTransform applyPost(const T &other) const

Applies other transform $T_\mathrm{o}$ after *this transform $T$ :

$T \circ T_\mathrm{o}$

template<typename Derived> Eigen::Matrix<double, 3, 1> transformPoint(const Eigen::MatrixBase<Derived> &point) const: Applies *this on 3D point.

template<typename Derived> Eigen::Matrix<double, 3, Derived::ColsAtCompileTime> transformCloud(const Eigen::MatrixBase<Derived> &cloud) const: Applies *this on 3D point cloud.

virtual double rotationNorm() const override

Returns:: the rotation norm in rad.

virtual double translationNorm() const override

Returns:: the translation norm.

inline const Eigen::Matrix<double, 4, 4> &getMatrix() const

Returns:: the homogeneous $\mathrm{SE(3)}$ transformation matrix.

inline Eigen::Matrix<double, 3, 1> getTranslation() const

Returns:: the translation vector.

inline Eigen::Matrix<double, 3, 3> getRotationMatrix() const

Returns:: the $\mathrm{SO(3)}$ rotation matrix.

template<typename Derived> MatrixTransform &setMatrix(const Eigen::MatrixBase<Derived> &matrix, bool unsafe = false): Sets the homogeneous $\mathrm{SE(3)}$ transformation matrix.

MatrixTransform &setTranslation(const Eigen::Matrix<double, 3, 1> &translation, bool unsafe = false): Sets the translation vector.

MatrixTransform &setRotationMatrix(const Eigen::Matrix<double, 3, 3> &rotation_matrix, bool unsafe = false): Sets the $\mathrm{SO(3)}$ rotation matrix.

inline virtual std::string desc() const override

Returns:: a description of *this.

virtual std::ostream &stream(std::ostream &os) const override: Inserts a description of *this.

template<class T> MatrixTransform &operator*=(const T &other): Applies other after *this.

template<class T> MatrixTransform &operator/=(const T &other): Applies the inverse of other after *this.

Public Static Functions

template<typename Derived> static bool isValidMatrix(const Eigen::MatrixBase<Derived> &matrix, double eps)

Checks if matrix is a valid rigid transformation matrix w.r.t.

the threshold eps.

template<typename Derived> static bool isValidRotationMatrix(const Eigen::MatrixBase<Derived> &matrix, double eps)

Checks if matrix is a valid rotation matrix w.r.t.

the threshold eps.

Private Members

Eigen::Matrix<double, 4, 4> matrix_: Homogeneous $\mathrm{SE(3)}$ transformation matrix.

class QuaternionTransform : public motion3d::TransformBase<QuaternionTransform>

Quaternion transformation consisting of a translation vector $\boldsymbol{t}$ and a rotation Quaternion $\mathrm{q}$ .

For representing a valid spatial transformation, the quaternion must be unit, i.e., $||\mathrm{q}|| = 1$ . An unsafe transform means that the validity check, usually performed at each operation, is skipped.

Operations:

Concatenation: $\mathrm{q}_{ac} = \mathrm{q}_{ab} \mathrm{q}_{bc}$ and $\{ 0, \boldsymbol{t}_{ac} \} = \{ 0, \boldsymbol{t}_{ab} \} + \mathrm{q}_{ab} \, \{ 0, \boldsymbol{t}_{bc} \} \, \mathrm{q}_{ab}^{\ast}$
Inversion: $V^{-1}: \mathrm{q}_{\mathrm{inv}} = \mathrm{q}^{\ast}$ and $\{ 0, \boldsymbol{t}_{\mathrm{inv}} \} = \mathrm{q}^{\ast} \, \{ 0, \boldsymbol{t} \} \, \mathrm{q}$
Point transformation: $\{ 0, \boldsymbol{p}_a \} = \mathrm{q}_{ab} \, \{ 0, \boldsymbol{p}_b \} \, \mathrm{q}_{ab}^{\ast} + \{ 0, \boldsymbol{t} \}$

Public Functions

DEFINE_POINTERS(QuaternionTransform)

QuaternionTransform(): Constructs and initializes a QuaternionTransform as identity transform.

template<typename Derived> QuaternionTransform(const Eigen::DenseBase<Derived> &translation, Quaternion<double> quaternion, bool unsafe = false): Constructs and initializes a QuaternionTransform from a translation vector and a rotation quaternion.

template<typename Derived> QuaternionTransform(const Eigen::DenseBase<Derived> &translation, const Eigen::Quaternion<double> &quaternion, bool unsafe = false): Constructs and initializes a QuaternionTransform from a translation vector and a rotation quaternion.

template<typename DerivedTrans, typename DerivedQuat> QuaternionTransform(const Eigen::DenseBase<DerivedTrans> &translation, const Eigen::DenseBase<DerivedQuat> &quaternion, bool unsafe = false): Constructs and initializes a QuaternionTransform from a translation vector and a rotation quaternion matrix.

explicit QuaternionTransform(const std::vector<std::uint8_t> &binary, bool unsafe = false)

Constructs and initializes a QuaternionTransform from binary data.

Throws:: InvalidTypeSizeException – for an invalid binary size.

explicit QuaternionTransform(const std::vector<double> &vector, bool unsafe = false)

Constructs and initializes a QuaternionTransform from vector data.

Throws:: InvalidTypeSizeException – for an invalid vector size.

template<typename Derived> explicit QuaternionTransform(const Eigen::DenseBase<Derived> &matrix, bool unsafe = false)

Constructs and initializes a QuaternionTransform from an Eigen vector matrix.

Throws:: InvalidTypeSizeException – for an invalid matrix size.

inline QuaternionTransform copy() const: Create a copy of *this.

QuaternionTransform &setIdentity(): Set *this to an identity transform.

virtual std::vector<double> toVector() const override: Converts *this to an std vector.

virtual Eigen::Matrix<double, Eigen::Dynamic, 1> toEigenVector() const override: Converts *this to an Eigen vector.

template<class T> T asType() const: Converts *this to transform type T.

virtual bool isValid(double eps) const override

Checks if *this is valid w.r.t.

the threshold eps.

QuaternionTransform &inverse_(): Inplace variant of inverse().

QuaternionTransform inverse() const

Returns:: the inverse transform to *this.

QuaternionTransform &normalized_(): Inplace variant of normalized().

QuaternionTransform normalized() const: Normalizes *this to a valid quaternion transform and sets unsafe to false.

QuaternionTransform &scaleTranslation_(double factor): Inplace variant of scaleTranslation().

QuaternionTransform scaleTranslation(double factor) const: Scales the translation by factor.

template<class T> QuaternionTransform &applyPre_(const T &other): Inplace variant of applyPre().

template<class T> QuaternionTransform applyPre(const T &other) const

Applies other transform $T_\mathrm{o}$ before *this transform $T$ :

$T_\mathrm{o} \circ T$

template<class T> QuaternionTransform &applyPost_(const T &other): Inplace variant of applyPost().

template<class T> QuaternionTransform applyPost(const T &other) const

Applies other transform $T_\mathrm{o}$ after *this transform $T$ :

$T \circ T_\mathrm{o}$

template<typename Derived> Eigen::Matrix<double, 3, 1> transformPoint(const Eigen::MatrixBase<Derived> &point) const: Applies *this on 3D point.

template<typename Derived> Eigen::Matrix<double, 3, Derived::ColsAtCompileTime> transformCloud(const Eigen::MatrixBase<Derived> &cloud) const: Applies *this on 3D point cloud.

virtual double rotationNorm() const override

Returns:: the rotation norm in rad.

virtual double translationNorm() const override

Returns:: the translation norm.

inline const Eigen::Matrix<double, 3, 1> &getTranslation() const

Returns:: the translation vector.

inline const Quaternion<double> &getQuaternion() const

Returns:: the rotation quaternion.

template<typename Derived> QuaternionTransform &setTranslation(const Eigen::MatrixBase<Derived> &translation, bool unsafe = false): Sets the translation vector.

QuaternionTransform &setQuaternion(const Quaternion<double> &quaternion, bool unsafe = false): Sets the rotation quaternion.

inline virtual std::string desc() const override

Returns:: a description of *this.

virtual std::ostream &stream(std::ostream &os) const override: Inserts a description of *this.

template<class T> QuaternionTransform &operator*=(const T &other): Applies other after *this.

template<class T> QuaternionTransform &operator/=(const T &other): Applies the inverse of other after *this.

Public Static Functions

static bool isUnitQuaternion(const Quaternion<double> &quaternion, double eps)

Checks if quaternion is unit w.r.t.

the threshold eps.

Private Members

Eigen::Matrix<double, 3, 1> translation_: Translation vector.

Quaternion<double> quaternion_: Rotation quaternion.