# template class mrpt::poses::CPoseOrPoint¶

The base template class for 2D & 3D points and poses.

This class use the Curiously Recurring Template Pattern (CRTP) to define a set of common methods to all the children classes without the cost of virtual methods. Since most important methods are inline, they will be expanded at compile time and optimized for every specific derived case.

For more information and examples, refer to the 2D/3D Geometry tutorial online.

## Introduction to 2D and 3D representation classes¶

There are two class of spatial representation classes:

Point: A point in the common mathematical sense, with no directional information.

2D: A 2D point is represented just by its coordinates (x,y).

3D: A 3D point is represented by its coordinates (x,y,z).

Pose: It is a point, plus a direction.

2D: A 2D pose is a 2D point plus a single angle, the yaw or φ angle: the angle from the positive X angle.

3D: A 3D point is a 3D point plus three orientation angles (More details above).

In the case for a 3D orientation many representation angles can be used (Euler angles,yaw/pitch/roll,…) but all of them can be handled by a 4x4 matrix called “Homogeneous Matrix”. This matrix includes both, the translation and the orientation for a point or a pose, and it can be obtained using the method getHomogeneousMatrix() which is defined for any pose or point. Note that when the YPR angles are used to define a 3D orientation, these three values can not be extracted from the matrix again.

**Homogeneous matrices:** These are 4x4 matrices which can represent any translation or rotation in 2D & 3D. See the tutorial online for more details. *

**Operators:** There are operators defined for the pose compounding \(\oplus\) and inverse pose compounding \(\ominus\) of poses and points. For example, let “a” and “b” be 2D or 3D poses. Then “a+b” returns the resulting pose of “moving b” from “a”; and “b-a” returns the pose of “b” as it is seen “from a”. They can be mixed points and poses, being 2D or 3D, in these operators, with the following results:

```
Does "a+b" return a Pose or a Point?
+---------------------------------+
| a \ b | Pose | Point |
+----------+-----------+----------+
| Pose | Pose | Point |
| Point | Pose | Point |
+---------------------------------+
```

```
Does "a-b" return a Pose or a Point?
+---------------------------------+
| a \ b | Pose | Point |
+----------+-----------+----------+
| Pose | Pose | Pose |
| Point | Point | Point |
+---------------------------------+
```

```
Does "a+b" and "a-b" return a 2D or 3D object?
+-------------------------+
| a \ b | 2D | 3D |
+----------+--------------+
| 2D | 2D | 3D |
| 3D | 3D | 3D |
+-------------------------+
```

```
```

See also:

#include <mrpt/poses/CPoseOrPoint.h> template <class DERIVEDCLASS, std::size_t DIM> class CPoseOrPoint: public mrpt::poses::detail::pose_point_impl { 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(); }; // direct descendants template <class DERIVEDCLASS, std::size_t DIM> class CPoint; template <class DERIVEDCLASS, std::size_t DIM> class CPose;