projective_trans_point_2dProjectiveTransPoint2dProjectiveTransPoint2dprojective_trans_point_2dT_projective_trans_point_2d🔗

Short description🔗

projective_trans_point_2dProjectiveTransPoint2dProjectiveTransPoint2dprojective_trans_point_2dT_projective_trans_point_2d — Project a homogeneous 2D point using a projective transformation matrix.

Signature🔗

projective_trans_point_2d( hom_mat2d HomMat2D, number Px, number Py, number Pw, out number Qx, out number Qy, out number Qw )

Description🔗

projective_trans_point_2dProjectiveTransPoint2d applies the homogeneous projective transformation matrix HomMat2DhomMat2Dhom_mat_2d to all homogeneous input points (Pxpxpx,Pypypy,Pwpwpw) and returns an array of homogeneous output points (Qxqxqx,Qyqyqy,Qwqwqw). The transformation is described by the homogeneous transformation matrix given in HomMat2DhomMat2Dhom_mat_2d. This corresponds to the following equation (input and output points as homogeneous vectors):

\[\begin{eqnarray*} \left( \begin{array}{c} \textrm{Qx} \\ \textrm{Qy} \\ \textrm{Qw} \end{array} \right) = \textrm{HomMat2D} \cdot \left( \begin{array}{c} \textrm{Px} \\ \textrm{Py} \\ \textrm{Pw} \end{array} \right) \end{eqnarray*}\]

To transform the homogeneous coordinates to Euclidean coordinates, they have to be divided by Qwqwqw:

\[\begin{eqnarray*} \left( \begin{array}{c} Ex \\ Ey \end{array} \right) = \left( \begin{array}{c} \frac{Qx}{Qw} \\ \frac{Qy}{Qw} \end{array} \right) \end{eqnarray*}\]

If the points to transform are specified in standard image coordinates, their row coordinates must be passed in Pxpxpx and their column coordinates in Pypypy. This is necessary to obtain a right-handed coordinate system for the image. In particular, this assures that rotations are performed in the correct direction. Note that the (\(x\),\(y\)) order of the matrices quite naturally corresponds to the usual (row,column) order for coordinates in the image.

Execution information🔗

Execution information

Multithreading type: reentrant (runs in parallel with non-exclusive operators).
Multithreading scope: global (may be called from any thread).
Automatically parallelized on internal data level.

Parameters🔗

HomMat2DhomMat2Dhom_mat_2d (input_control) hom_mat2d → (real)HTuple (double)HHomMat2D, HTuple (double)Sequence[float]Htuple (double)

Homogeneous projective transformation matrix.

Pxpxpx (input_control) number(-array) → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)MaybeSequence[Union[float, int]]Htuple (double / Hlong)

Input point (x coordinate).

Pypypy (input_control) number(-array) → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)MaybeSequence[Union[float, int]]Htuple (double / Hlong)

Input point (y coordinate).

Pwpwpw (input_control) number(-array) → (real / integer)HTuple (double / Hlong)HTuple (double / int / long)MaybeSequence[Union[float, int]]Htuple (double / Hlong)

Input point (w coordinate).

Qxqxqx (output_control) number(-array) → (real)HTuple (double)HTuple (double)Sequence[float]Htuple (double)

Output point (x coordinate).

Qyqyqy (output_control) number(-array) → (real)HTuple (double)HTuple (double)Sequence[float]Htuple (double)

Output point (y coordinate).

Qwqwqw (output_control) number(-array) → (real)HTuple (double)HTuple (double)Sequence[float]Htuple (double)

Output point (w coordinate).

Combinations with other operators🔗

Combinations

Possible predecessors

vector_to_proj_hom_mat2dVectorToProjHomMat2d, hom_vector_to_proj_hom_mat2dHomVectorToProjHomMat2d, proj_match_points_ransacProjMatchPointsRansac, proj_match_points_ransac_guidedProjMatchPointsRansacGuided, hom_mat3d_projectHomMat3dProject

Module🔗

Foundation