Apply an arbitrary affine 2D transformation to XLD contours.

affine_trans_contour_xld applies an arbitrary affine 2D transformation, i.e., scaling, rotation, translation, and slant (skewing), to the XLD contours given in Contours and returns the transformed contours in ContoursAffinTrans. The affine transformation is described by the homogeneous transformation matrix given in HomMat2D, which can be created using the operators hom_mat2d_identity, hom_mat2d_scale, hom_mat2d_rotate, hom_mat2d_translate, etc., or be the result of operators like vector_angle_to_rigid.

The components of the homogeneous transformation matrix are interpreted as follows: The row coordinate of the image corresponds to x and the col coordinate corresponds to y of the coordinate system in which the transformation matrix was defined. 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.

The used coordinate system is the same as in affine_trans_pixel. This means that in fact not HomMat2D is applied but a modified version. Therefore, applying affine_trans_contour_xld corresponds to the following chain of transformations, which is applied to each point (Row_i, Col_i) of the contour (input and output pixels as homogeneous vectors):

  / RowTrans_i \   / 1 0 -0.5 \              / 1 0 +0.5 \   / Row_i \
  | ColTrans_i | = | 0 1 -0.5 | * HomMat2D * | 0 1 +0.5 | * | Col_i |
  \    1       /   \ 0 0   1  /              \ 0 0   1  /   \  1    /

As an effect, you might get unexpected results when creating affine transformations based on coordinates that are derived from the contour, e.g., by operators like area_center_xld. For example, if you use this operator to calculate the center of gravity of a rotationally symmetric XLD contour and then rotate the contour around this point using hom_mat2d_rotate, the resulting contour will not lie on the original one. In such a case, you can compensate this effect by applying the following translations to HomMat2D before using it in affine_trans_contour_xld:

  hom_mat2d_translate(HomMat2D, 0.5, 0.5, HomMat2DTmp)
  hom_mat2d_translate_local(HomMat2DTmp, -0.5, -0.5, HomMat2DAdapted)
  affine_trans_contour_xld(Contours, ContoursAffinTrans, HomMat2DAdapted)

If the matrix HomMat2D represents an affine transformation (i.e., not a projective transformation), affine_trans_contour_xld returns 2 (H_MSG_TRUE). If the input is empty the behavior can be set via set_system(::'no_object_result',<Result>:). If necessary, an exception handling is raised.

affine_trans_contour_xld is reentrant and automatically parallelized (on tuple level).

hom_mat2d_identity, hom_mat2d_translate, hom_mat2d_rotate, hom_mat2d_scale

affine_trans_image, affine_trans_region

Foundation