project_hom_point_hom_mat3dT_project_hom_point_hom_mat3dProjectHomPointHomMat3dProjectHomPointHomMat3d (Operator)

Name

project_hom_point_hom_mat3dT_project_hom_point_hom_mat3dProjectHomPointHomMat3dProjectHomPointHomMat3d — Project a homogeneous 3D point using a 3×4 projection matrix.

Signature

project_hom_point_hom_mat3d( : : HomMat3D, Px, Py, Pz, Pw : Qx, Qy, Qw)

Description

projective_trans_hom_point_3dprojective_trans_hom_point_3dProjectiveTransHomPoint3dProjectiveTransHomPoint3dProjectiveTransHomPoint3d applies the 3×4 projection matrix HomMat3DHomMat3DHomMat3DHomMat3DhomMat3D to all homogeneous input points (PxPxPxPxpx,PyPyPyPypy,PzPzPzPzpz,PwPwPwPwpw) and returns an array of homogeneous output points (QxQxQxQxqx,QyQyQyQyqy,QwQwQwQwqw). The transformation is described by the homogeneous transformation matrix given in HomMat3DHomMat3DHomMat3DHomMat3DhomMat3D. This corresponds to the following equation (input and output points as homogeneous vectors):

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

This can be achieved directly by calling project_point_hom_mat3dproject_point_hom_mat3dProjectPointHomMat3dProjectPointHomMat3dProjectPointHomMat3d. Thus, project_hom_point_hom_mat3dproject_hom_point_hom_mat3dProjectHomPointHomMat3dProjectHomPointHomMat3dProjectHomPointHomMat3d is primarily useful for transforming points or point sets for which the resulting points might lie on the line at infinity, i.e., points that potentially have QwQwQwQwqw = 0, for which the above division cannot be performed.

Note that, consistent with the conventions used by the projection in calibrate_camerascalibrate_camerasCalibrateCamerasCalibrateCamerasCalibrateCameras, QxQxQxQxqx corresponds to the column coordinate of an image and QyQyQyQyqy corresponds to the row coordinate.