# class mrpt::poses::CPose3D

A SE(3) pose, comprising a 3D translation and a 3D rotation.

The transformation is stored in two separate containers:

• a 3-array for the translation ∈ R³, and

• a 3x3 rotation matrix ∈ SO(3).

This class allows parameterizing 6D poses as a 6-vector [x y z yaw pitch roll] (read below for the angles convention). Note however, that the yaw/pitch/roll angles are only computed (on-demand and transparently) when the user requests them. Normally, rotations and transformations are always handled via the 3x3 SO(3) rotation matrix.

Yaw/Pitch/Roll angles are defined as successive rotations around local (dynamic) axes in the Z/Y/X order: It can be shown that “yaw, pitch, roll” can be also understood as rotations around global (static) axes. Both conventions lead to exactly the same SE(3) transformations, although in it is conventional to write the numbers in reverse order. That is, the same SO(3) rotation can be described equivalently with any of these two parameterizations:

• In local axes Z/Y/X convention: [yaw pitch roll] (This is the convention used in mrpt::poses::CPose3D)

• In global axes X/Y/Z convention: [roll pitch yaw] (One of the Euler angles conventions)

For further descriptions of point & pose classes, see mrpt::poses::CPoseOrPoint or refer to the 2D/3D Geometry tutorial online.

To change the individual components of the pose, use CPose3D::setFromValues. This class assures that the internal SO(3) rotation matrix is always up-to-date with the “yaw pitch roll” members.

Rotations in 3D can be also represented by quaternions. See mrpt::math::CQuaternion, and method CPose3D::getAsQuaternion.

This class and CPose3DQuat are very similar, and they can be converted to the each other automatically via transformation constructors.

For Lie algebra methods, see mrpt::poses::Lie.

Read also: “A tutorial on SE(3) transformation parameterizations and on-manifold optimization”, in 

#include <mrpt/poses/CPose3D.h>

class CPose3D:
public mrpt::poses::CPose,
public mrpt::serialization::CSerializable,
public mrpt::Stringifyable
{
public:
// typedefs

typedef double value_type;
typedef double& reference;
typedef double const_reference;
typedef std::size_t size_type;
typedef std::ptrdiff_t difference_type;
typedef CPose3D type_value;

// enums

enum
{
is_3D_val = 1,
};

enum
{
rotation_dimensions = 3,
};

enum
{
is_PDF_val = 0,
};

enum
{
static_size = 6,
};

//
fields

mrpt::math::CVectorFixedDouble<3> m_coords;

// construction

CPose3D();

CPose3D(
const double x,
const double y,
const double z,
const double yaw = 0,
const double pitch = 0,
const double roll = 0
);

CPose3D(const math::CMatrixDouble& m);
CPose3D(const math::CMatrixDouble44& m);

template <class MATRIX33, class VECTOR3>
CPose3D(
const MATRIX33& rot,
const VECTOR3& xyz
);

CPose3D(const mrpt::math::CMatrixDouble33& rot, const mrpt::math::CVectorFixedDouble<3>& xyz);
CPose3D(const CPose2D& p);
CPose3D(const CPoint3D& p);
CPose3D(const mrpt::math::TPose3D& o);
CPose3D(const mrpt::math::CQuaternionDouble& q, const double x, const double y, const double z);
CPose3D(const CPose3DQuat& p);
CPose3D(TConstructorFlags_Poses);
CPose3D(const mrpt::math::CVectorFixedDouble<12>& vec12);

//
methods

mrpt::math::TPose3D asTPose() const;
static CPose3D Identity();

static CPose3D FromXYZYawPitchRoll(
double x,
double y,
double z,
double yaw,
double pitch,
double roll
);

static CPose3D FromYawPitchRoll(double yaw, double pitch, double roll);
static CPose3D FromTranslation(double x, double y, double z);
static CPose3D FromTranslation(const mrpt::math::TPoint3D& t);

template <class MATRIX>
static CPose3D FromHomogeneousMatrix(const MATRIX& m);

template <class MATRIX, class VECTOR>
static CPose3D FromRotationAndTranslation(
const MATRIX& rot,
const VECTOR& t
);

static CPose3D FromQuaternion(const mrpt::math::CQuaternionDouble& q);
static CPose3D FromQuaternionAndTranslation(const mrpt::math::CQuaternionDouble& q, double x, double y, double z);

template <typename Point3DLike>
static CPose3D FromQuaternionAndTranslation(
const mrpt::math::CQuaternionDouble& q,
const Point3DLike& pt
);

void getHomogeneousMatrix(mrpt::math::CMatrixDouble44& out_HM) const;
void getRotationMatrix(mrpt::math::CMatrixDouble33& ROT) const;
const mrpt::math::CMatrixDouble33& getRotationMatrix() const;
void setRotationMatrix(const mrpt::math::CMatrixDouble33& ROT);
mrpt::math::TPoint3D translation() const;
CPose3D operator + (const CPose3D& b) const;
CPoint3D operator + (const CPoint3D& b) const;
CPoint3D operator + (const CPoint2D& b) const;
void sphericalCoordinates(const mrpt::math::TPoint3D& point, double& out_range, double& out_yaw, double& out_pitch) const;

void composePoint(
double lx,
double ly,
double lz,
double& gx,
double& gy,
double& gz,
mrpt::optional_ref<mrpt::math::CMatrixDouble33> out_jacobian_df_dpoint = std::nullopt,
mrpt::optional_ref<mrpt::math::CMatrixDouble36> out_jacobian_df_dpose = std::nullopt,
mrpt::optional_ref<mrpt::math::CMatrixDouble36> out_jacobian_df_dse3 = std::nullopt,
bool use_small_rot_approx = false
) const;

void composePoint(const mrpt::math::TPoint3D& local_point, mrpt::math::TPoint3D& global_point) const;
mrpt::math::TPoint3D composePoint(const mrpt::math::TPoint3D& l) const;
void composePoint(const mrpt::math::TPoint3D& local_point, mrpt::math::TPoint2D& global_point) const;
void composePoint(double lx, double ly, double lz, float& gx, float& gy, float& gz) const;
mrpt::math::TVector3D rotateVector(const mrpt::math::TVector3D& local) const;
mrpt::math::TVector3D inverseRotateVector(const mrpt::math::TVector3D& global) const;

void inverseComposePoint(
const double gx,
const double gy,
const double gz,
double& lx,
double& ly,
double& lz,
mrpt::optional_ref<mrpt::math::CMatrixDouble33> out_jacobian_df_dpoint = std::nullopt,
mrpt::optional_ref<mrpt::math::CMatrixDouble36> out_jacobian_df_dpose = std::nullopt,
mrpt::optional_ref<mrpt::math::CMatrixDouble36> out_jacobian_df_dse3 = std::nullopt
) const;

void inverseComposePoint(const mrpt::math::TPoint3D& g, mrpt::math::TPoint3D& l) const;
mrpt::math::TPoint3D inverseComposePoint(const mrpt::math::TPoint3D& g) const;
void inverseComposePoint(const mrpt::math::TPoint2D& g, mrpt::math::TPoint2D& l, const double eps = 1e-6) const;
void composeFrom(const CPose3D& A, const CPose3D& B);
CPose3D& operator += (const CPose3D& b);
void inverseComposeFrom(const CPose3D& A, const CPose3D& B);
CPose3D operator - (const CPose3D& b) const;
void inverse();
void changeCoordinatesReference(const CPose3D& p);
void normalizeAngles();
void operator *= (const double s);

void setFromValues(
const double x0,
const double y0,
const double z0,
const double yaw = 0,
const double pitch = 0,
const double roll = 0
);

template <typename VECTORLIKE>
void setFromXYZQ(
const VECTORLIKE& v,
const size_t index_offset = 0
);

void setYawPitchRoll(const double yaw_, const double pitch_, const double roll_);

template <class ARRAYORVECTOR>
void setFrom12Vector(const ARRAYORVECTOR& vec12);

template <class ARRAYORVECTOR>
void getAs12Vector(ARRAYORVECTOR& vec12) const;

void getYawPitchRoll(double& yaw, double& pitch, double& roll) const;
double yaw() const;
double pitch() const;
double roll() const;
void asVector(vector_t& v) const;
void getAsQuaternion(mrpt::math::CQuaternionDouble& q, mrpt::optional_ref<mrpt::math::CMatrixDouble43> out_dq_dr = std::nullopt) const;
double operator [] (unsigned int i) const;
virtual std::string asString() const;
void fromString(const std::string& s);
void fromStringRaw(const std::string& s);
bool isHorizontal(const double tolerance = 0) const;
double distanceEuclidean6D(const CPose3D& o) const;
static CPose3D FromString(const std::string& s);
static constexpr size_type size();
static constexpr bool empty();
static constexpr size_type max_size();
static void resize(const size_t n);
CPose3D getOppositeScalar() const;
virtual void setToNaN();
const type_value& getPoseMean() const;
type_value& getPoseMean();
static constexpr bool is_3D();
static constexpr bool is_PDF();
};

## Inherited Members

public:
//
methods

double& x();
double& y();
void x(const double v);
void y(const double v);
void x_incr(const double v);
void y_incr(const double v);
const DERIVEDCLASS& derived() const;
DERIVEDCLASS& derived();

## Typedefs

typedef double value_type

The type of the elements.

typedef CPose3D type_value

Used to emulate CPosePDF types, for example, in mrpt::graphs::CNetworkOfPoses.

## Fields

mrpt::math::CVectorFixedDouble<3> m_coords

The translation vector [x,y,z] access directly or with x(), y(), z() setter/getter methods.

## Construction

CPose3D()

Default constructor, with all the coordinates set to zero.

CPose3D(
const double x,
const double y,
const double z,
const double yaw = 0,
const double pitch = 0,
const double roll = 0
)

Constructor with initilization of the pose, translation (x,y,z) in meters, (yaw,pitch,roll) angles in radians.

FromXYZYawPitchRoll()

CPose3D(const math::CMatrixDouble& m)

Constructor from a 4x4 homogeneous matrix - the passed matrix can be actually of any size larger than or equal 3x4, since only those first values are used (the last row of a homogeneous 4x4 matrix are always fixed).

CPose3D(const math::CMatrixDouble44& m)

Constructor from a 4x4 homogeneous matrix:

template <class MATRIX33, class VECTOR3>
CPose3D(
const MATRIX33& rot,
const VECTOR3& xyz
)

Constructor from a 3x3 rotation matrix and a the translation given as a 3-vector, a 3-array, a CPoint3D or a mrpt::math::TPoint3D.

CPose3D(const mrpt::math::CMatrixDouble33& rot, const mrpt::math::CVectorFixedDouble<3>& xyz)

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

CPose3D(const CPose2D& p)

Constructor from a CPose2D object.

CPose3D(const CPoint3D& p)

Constructor from a CPoint3D object.

CPose3D(const mrpt::math::TPose3D& o)

Constructor from lightweight object.

CPose3D(const mrpt::math::CQuaternionDouble& q, const double x, const double y, const double z)

Constructor from a quaternion (which only represents the 3D rotation part) and a 3D displacement.

CPose3D(const CPose3DQuat& p)

Constructor from a CPose3DQuat.

Constructor from a quaternion-based full pose.

CPose3D(TConstructorFlags_Poses)

Fast constructor that leaves all the data uninitialized - call with UNINITIALIZED_POSE as argument.

CPose3D(const mrpt::math::CVectorFixedDouble<12>& vec12)

Constructor from an array with these 12 elements: [r11 r21 r31 r12 r22 r32 r13 r23 r33 tx ty tz] where r{ij} are the entries of the 3x3 rotation matrix and t{x,y,z} are the 3D translation of the pose.

## Methods

static CPose3D Identity()

Returns the identity transformation.

static CPose3D FromXYZYawPitchRoll(
double x,
double y,
double z,
double yaw,
double pitch,
double roll
)

Builds a pose from a translation (x,y,z) in meters and (yaw,pitch,roll) angles in radians.

(New in MRPT 2.1.8)

static CPose3D FromYawPitchRoll(double yaw, double pitch, double roll)

Builds a pose with a null translation and (yaw,pitch,roll) angles in radians.

(New in MRPT 2.1.8)

static CPose3D FromTranslation(double x, double y, double z)

Builds a pose with a translation without rotation.

(New in MRPT 2.1.8)

template <class MATRIX>
static CPose3D FromHomogeneousMatrix(const MATRIX& m)

Builds a pose with a 4x4 homogeneous matrix.

(New in MRPT 2.1.8)

template <class MATRIX, class VECTOR>
static CPose3D FromRotationAndTranslation(
const MATRIX& rot,
const VECTOR& t
)

Builds a pose with a 3x3 SO(3) rotation matrix and a translation vector.

(New in MRPT 2.1.8)

static CPose3D FromQuaternion(const mrpt::math::CQuaternionDouble& q)

Builds a pose from a quaternion (and no translation).

(New in MRPT 2.1.8)

static CPose3D FromQuaternionAndTranslation(
const mrpt::math::CQuaternionDouble& q,
double x,
double y,
double z
)

Builds a pose from a quaternion and a (x,y,z) translation.

(New in MRPT 2.1.8)

template <typename Point3DLike>
static CPose3D FromQuaternionAndTranslation(
const mrpt::math::CQuaternionDouble& q,
const Point3DLike& pt
)

Builds a pose from a quaternion and a 3D translation.

(New in MRPT 2.3.3)

void getHomogeneousMatrix(mrpt::math::CMatrixDouble44& out_HM) const

Returns the corresponding 4x4 homogeneous transformation matrix for the point(translation) or pose (translation+orientation).

void getRotationMatrix(mrpt::math::CMatrixDouble33& ROT) const

Get the 3x3 rotation matrix.

getHomogeneousMatrix

const mrpt::math::CMatrixDouble33& getRotationMatrix() const

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

void setRotationMatrix(const mrpt::math::CMatrixDouble33& ROT)

Sets the 3x3 rotation matrix.

mrpt::math::TPoint3D translation() const

Returns the (x,y,z) translational part of the SE(3) transformation.

CPose3D operator + (const CPose3D& b) const

The operator $$a \oplus b$$ is the pose compounding operator.

CPoint3D operator + (const CPoint3D& b) const

The operator $$a \oplus b$$ is the pose compounding operator.

CPoint3D operator + (const CPoint2D& b) const

The operator $$a \oplus b$$ is the pose compounding operator.

void sphericalCoordinates(
const mrpt::math::TPoint3D& point,
double& out_range,
double& out_yaw,
double& out_pitch
) const

Computes the spherical coordinates of a 3D point as seen from the 6D pose specified by this object.

void composePoint(
double lx,
double ly,
double lz,
double& gx,
double& gy,
double& gz,
mrpt::optional_ref<mrpt::math::CMatrixDouble33> out_jacobian_df_dpoint = std::nullopt,
mrpt::optional_ref<mrpt::math::CMatrixDouble36> out_jacobian_df_dpose = std::nullopt,
mrpt::optional_ref<mrpt::math::CMatrixDouble36> out_jacobian_df_dse3 = std::nullopt,
bool use_small_rot_approx = false
) const

An alternative, slightly more efficient way of doing $$G = P \oplus L$$ with G and L being 3D points and P this 6D pose.

If pointers are provided, the corresponding Jacobians are returned. “out_jacobian_df_dse3” stands for the Jacobian with respect to the 6D locally Euclidean vector in the tangent space of SE(3). See this report for mathematical details.

Parameters:

 If set to true, the Jacobian “out_jacobian_df_dpose” uses a fastest linearized appoximation (valid only for small rotations!).
void composePoint(const mrpt::math::TPoint3D& local_point, mrpt::math::TPoint3D& global_point) const

An alternative, slightly more efficient way of doing $$G = P \oplus L$$ with G and L being 3D points and P this 6D pose.

local_point is passed by value to allow global and local point to be the same variable

mrpt::math::TPoint3D composePoint(const mrpt::math::TPoint3D& l) const

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

void composePoint(const mrpt::math::TPoint3D& local_point, mrpt::math::TPoint2D& global_point) const

This version of the method assumes that the resulting point has no Z component (use with caution!)

void composePoint(
double lx,
double ly,
double lz,
float& gx,
float& gy,
float& gz
) const

An alternative, slightly more efficient way of doing $$G = P \oplus L$$ with G and L being 3D points and P this 6D pose.

mrpt::math::TVector3D rotateVector(const mrpt::math::TVector3D& local) const

Rotates a vector (i.e.

like composePoint(), but ignoring translation)

mrpt::math::TVector3D inverseRotateVector(const mrpt::math::TVector3D& global) const

Inverse of rotateVector(), i.e.

using the inverse rotation matrix

void inverseComposePoint(
const double gx,
const double gy,
const double gz,
double& lx,
double& ly,
double& lz,
mrpt::optional_ref<mrpt::math::CMatrixDouble33> out_jacobian_df_dpoint = std::nullopt,
mrpt::optional_ref<mrpt::math::CMatrixDouble36> out_jacobian_df_dpose = std::nullopt,
mrpt::optional_ref<mrpt::math::CMatrixDouble36> out_jacobian_df_dse3 = std::nullopt
) const

Computes the 3D point L such as $$L = G \ominus this$$.

If pointers are provided, the corresponding Jacobians are returned. “out_jacobian_df_dse3” stands for the Jacobian with respect to the 6D locally Euclidean vector in the tangent space of SE(3). See this report for mathematical details.

void inverseComposePoint(const mrpt::math::TPoint3D& g, mrpt::math::TPoint3D& l) const

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

mrpt::math::TPoint3D inverseComposePoint(const mrpt::math::TPoint3D& g) const

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

void inverseComposePoint(const mrpt::math::TPoint2D& g, mrpt::math::TPoint2D& l, const double eps = 1e-6) const

Parameters:

 If the z component of the result is greater than some epsilon
void composeFrom(const CPose3D& A, const CPose3D& B)

Makes “this = A (+) B”; this method is slightly more efficient than “this= A + B;” since it avoids the temporary object.

A or B can be “this” without problems.

CPose3D& operator += (const CPose3D& b)

Make $$this = this \oplus b$$ (b can be “this” without problems)

void inverseComposeFrom(const CPose3D& A, const CPose3D& B)

Makes $$this = A \ominus B$$ this method is slightly more efficient than “this= A - B;” since it avoids the temporary object.

A or B can be “this” without problems.

CPose3D operator - (const CPose3D& b) const

Compute $$RET = this \oplus b$$.

void inverse()

Convert this pose into its inverse, saving the result in itself.

operator-

void changeCoordinatesReference(const CPose3D& p)

makes: this = p (+) this

void addComponents(const CPose3D& p)

Scalar sum of all 6 components: This is diferent from poses composition, which is implemented as “+” operators.

normalizeAngles

void normalizeAngles()

Rebuild the internal matrix & update the yaw/pitch/roll angles within the ]-PI,PI] range (Must be called after using addComponents)

void operator *= (const double s)

Scalar multiplication of x,y,z,yaw,pitch & roll (angles will be wrapped to the ]-pi,pi] interval).

void setFromValues(
const double x0,
const double y0,
const double z0,
const double yaw = 0,
const double pitch = 0,
const double roll = 0
)

Set the pose from a 3D position (meters) and yaw/pitch/roll angles (radians) - This method recomputes the internal rotation matrix.

template <typename VECTORLIKE>
void setFromXYZQ(
const VECTORLIKE& v,
const size_t index_offset = 0
)

Set the pose from a 3D position (meters) and a quaternion, stored as [x y z qr qx qy qz] in a 7-element vector.

setFromValues, getYawPitchRoll, setYawPitchRoll, CQuaternion, getAsQuaternion

void setYawPitchRoll(const double yaw_, const double pitch_, const double roll_)

Set the 3 angles of the 3D pose (in radians) - This method recomputes the internal rotation coordinates matrix.

template <class ARRAYORVECTOR>
void setFrom12Vector(const ARRAYORVECTOR& vec12)

Set pose from an array with these 12 elements: [r11 r21 r31 r12 r22 r32 r13 r23 r33 tx ty tz] where r{ij} are the entries of the 3x3 rotation matrix and t{x,y,z} are the 3D translation of the pose.

getAs12Vector

template <class ARRAYORVECTOR>
void getAs12Vector(ARRAYORVECTOR& vec12) const

Get the pose representation as an array with these 12 elements: [r11 r21 r31 r12 r22 r32 r13 r23 r33 tx ty tz] where r{ij} are the entries of the 3x3 rotation matrix and t{x,y,z} are the 3D translation of the pose.

setFrom12Vector

void getYawPitchRoll(double& yaw, double& pitch, double& roll) const

Returns the three angles (yaw, pitch, roll), in radians, from the rotation matrix.

double yaw() const

Get the YAW angle (in radians)

setFromValues

double pitch() const

Get the PITCH angle (in radians)

setFromValues

double roll() const

Get the ROLL angle (in radians)

setFromValues

void asVector(vector_t& v) const

Returns a 6x1 vector with [x y z yaw pitch roll]’.

void getAsQuaternion(mrpt::math::CQuaternionDouble& q, mrpt::optional_ref<mrpt::math::CMatrixDouble43> out_dq_dr = std::nullopt) const

Returns the quaternion associated to the rotation of this object (NOTE: XYZ translation is ignored)

$\begin{split}\mathbf{q} = \left( \begin{array}{c} \cos (\phi /2) \cos (\theta /2) \cos (\psi /2) + \sin (\phi /2) \sin (\theta /2) \sin (\psi /2) \\ \sin (\phi /2) \cos (\theta /2) \cos (\psi /2) - \cos (\phi /2) \sin (\theta /2) \sin (\psi /2) \\ \cos (\phi /2) \sin (\theta /2) \cos (\psi /2) + \sin (\phi /2) \cos (\theta /2) \sin (\psi /2) \\ \cos (\phi /2) \cos (\theta /2) \sin (\psi /2) - \sin (\phi /2) \sin (\theta /2) \cos (\psi /2) \\ \end{array}\right)\end{split}$

With : $$\phi = roll$$, $$\theta = pitch$$ and $$\psi = yaw$$.

Parameters:

 out_dq_dr If provided, the 4x3 Jacobian of the transformation will be computed and stored here. It’s the Jacobian of the transformation from (yaw pitch roll) to (qr qx qy qz).
virtual std::string asString() const

Returns a human-readable textual representation of the object (eg: “[x y z yaw pitch roll]”, angles in degrees.)

fromString

void fromString(const std::string& s)

Set the current object value from a string generated by ‘asString’ (eg: “[x y z yaw pitch roll]”, angles in deg.

)

Parameters:

 std::exception On invalid format

asString

void fromStringRaw(const std::string& s)

Same as fromString, but without requiring the square brackets in the string.

bool isHorizontal(const double tolerance = 0) const

Return true if the 6D pose represents a Z axis almost exactly vertical (upwards or downwards), with a given tolerance (if set to 0 exact horizontality is tested).

double distanceEuclidean6D(const CPose3D& o) const

The euclidean distance between two poses taken as two 6-length vectors (angles in radians).

CPose3D getOppositeScalar() const

Return the opposite of the current pose instance by taking the negative of all its components individually.

virtual void setToNaN()

Set all data fields to quiet NaN.