projective_trans_point_2dT_projective_trans_point_2dProjectiveTransPoint2dProjectiveTransPoint2d (Operator)

Name

projective_trans_point_2dT_projective_trans_point_2dProjectiveTransPoint2dProjectiveTransPoint2d — Project a homogeneous 2D point using a projective transformation matrix.

Signature

projective_trans_point_2d( : : HomMat2D, Px, Py, Pw : Qx, Qy, Qw)

projective_trans_point_2dprojective_trans_point_2dProjectiveTransPoint2dProjectiveTransPoint2dProjectiveTransPoint2d applies the homogeneous projective transformation matrix HomMat2DHomMat2DHomMat2DHomMat2DhomMat2D to all homogeneous input points (PxPxPxPxpx,PyPyPyPypy,PwPwPwPwpw) and returns an array of homogeneous output points (QxQxQxQxqx,QyQyQyQyqy,QwQwQwQwqw). The transformation is described by the homogeneous transformation matrix given in HomMat2DHomMat2DHomMat2DHomMat2DhomMat2D. This corresponds to the following equation (input and output points as homogeneous vectors):

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

If the points to transform are specified in standard image coordinates, their row coordinates must be passed in PxPxPxPxpx and their column coordinates in PyPyPyPypy. 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.