Operators

# projective_trans_hom_point_3d (Operator)

## Name

projective_trans_hom_point_3d — Project a homogeneous 3D point using a projective transformation matrix.

## Signature

projective_trans_hom_point_3d( : : HomMat3D, Px, Py, Pz, Pw : Qx, Qy, Qz, Qw)

## Description

projective_trans_hom_point_3d applies the homogeneous projective transformation matrix HomMat3D to all homogeneous input points (Px,Py,Pz,Pw) and returns an array of homogeneous output points (Qx,Qy,Qz,Qw). The transformation is described by the homogeneous transformation matrix given in HomMat3D. This corresponds to the following equation (input and output points as homogeneous vectors):

```  / Qx \              / Px \
| Qy | = HomMat3D * | Py |
| Qz |              | Pz |
\ Qw /              \ Pw /
```

To transform the homogeneous coordinates to Euclidean coordinates, they must be divided by Qw:

```(Ex,Ey,Ez) = (Qx/Qw,Qy/Qw,Qz/Qw)
```

This can be achieved directly by calling projective_trans_point_3d. Thus, projective_trans_hom_point_3d is primarily useful for transforming points or point sets for which the resulting points might lie in the plane at infinity, i.e., points that potentially have Qw = 0, for which the above division cannot be performed.

## Parallelization

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Processed without parallelization.

## Parameters

HomMat3D (input_control)  hom_mat3d (real)

Homogeneous projective transformation matrix.

Px (input_control)  number(-array) (real / integer)

Input point (x coordinate).

Py (input_control)  number(-array) (real / integer)

Input point (y coordinate).

Pz (input_control)  number(-array) (real / integer)

Input point (z coordinate).

Pw (input_control)  number(-array) (real / integer)

Input point (w coordinate).

Qx (output_control)  number(-array) (real)

Output point (x coordinate).

Qy (output_control)  number(-array) (real)

Output point (y coordinate).

Qz (output_control)  number(-array) (real)

Output point (z coordinate).

Qw (output_control)  number(-array) (real)

Output point (w coordinate).

## Module

Foundation

 Operators