affine_trans_polygon_xldT_affine_trans_polygon_xldaffine_trans_polygon_xldAffineTransPolygonXldAffineTransPolygonXld (Operator)

Name

affine_trans_polygon_xldT_affine_trans_polygon_xldaffine_trans_polygon_xldAffineTransPolygonXldAffineTransPolygonXld — Apply an arbitrary affine transformation to XLD polygons.

Signature

Description

affine_trans_polygon_xldaffine_trans_polygon_xldaffine_trans_polygon_xldAffineTransPolygonXldAffineTransPolygonXld applies an arbitrary affine transformation, i.e., scaling, rotation, translation, and slant (skewing), to the XLD polygons given in PolygonsPolygonsPolygonsPolygonspolygons and returns the transformed polygons in PolygonsAffinTransPolygonsAffinTransPolygonsAffinTransPolygonsAffinTranspolygonsAffinTrans. The affine transformation is described by the homogeneous transformation matrix given in HomMat2DHomMat2DHomMat2DHomMat2DhomMat2D. This matrix can be created using the operators hom_mat2d_identityhom_mat2d_identityhom_mat2d_identityHomMat2dIdentityHomMat2dIdentity, hom_mat2d_scalehom_mat2d_scalehom_mat2d_scaleHomMat2dScaleHomMat2dScale, hom_mat2d_rotatehom_mat2d_rotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotate, hom_mat2d_translatehom_mat2d_translatehom_mat2d_translateHomMat2dTranslateHomMat2dTranslate, etc., or be the result of operators like vector_angle_to_rigidvector_angle_to_rigidvector_angle_to_rigidVectorAngleToRigidVectorAngleToRigid.

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.

Attention

The XLD contours that are possibly referenced by PolygonsPolygonsPolygonsPolygonspolygons are neither transformed nor stored with the output polygons, since this is generally impossible without creating inconsistencies for the attributes of the XLD contours. Hence, operators that access the contours associated with a polygon, e.g., split_contours_xldsplit_contours_xldsplit_contours_xldSplitContoursXldSplitContoursXld will not work correctly.

The used coordinate system is the same as in affine_trans_pixelaffine_trans_pixelaffine_trans_pixelAffineTransPixelAffineTransPixel. This means that in fact not HomMat2DHomMat2DHomMat2DHomMat2DhomMat2D is applied but a modified version. Therefore, applying affine_trans_polygon_xldaffine_trans_polygon_xldaffine_trans_polygon_xldAffineTransPolygonXldAffineTransPolygonXld corresponds to a chain of transformations (see affine_trans_pixelaffine_trans_pixelaffine_trans_pixelAffineTransPixelAffineTransPixel), which is applied to each point of the polygon (input and output pixels as homogeneous vectors). As an effect, you might get unexpected results when creating affine transformations based on coordinates that are derived from the polygon, e.g., by operators like area_center_xldarea_center_xldarea_center_xldAreaCenterXldAreaCenterXld. For example, if you use this operator to calculate the center of gravity of a rotationally symmetric XLD polygon and then rotate the polygon around this point using hom_mat2d_rotatehom_mat2d_rotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotate, the resulting polygon will not lie on the original one. In such a case, you can compensate this effect by applying the following translations to HomMat2DHomMat2DHomMat2DHomMat2DhomMat2D before using it in affine_trans_polygon_xldaffine_trans_polygon_xldaffine_trans_polygon_xldAffineTransPolygonXldAffineTransPolygonXld:

  hom_mat2d_translate(HomMat2D, 0.5, 0.5, HomMat2DTmp)
  hom_mat2d_translate_local(HomMat2DTmp, -0.5, -0.5, HomMat2DAdapted)
  affine_trans_polygon_xld(Polygons, PolygonsAffinTrans, HomMat2DAdapted)

Parallelization

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

Parameters

Result

If the matrix HomMat2DHomMat2DHomMat2DHomMat2DhomMat2D represents an affine transformation (i.e., not a projective transformation), affine_trans_polygon_xldaffine_trans_polygon_xldaffine_trans_polygon_xldAffineTransPolygonXldAffineTransPolygonXld returns 2 (H_MSG_TRUE). If the input is empty the behavior can be set via set_system(::'no_object_result',<Result>:)set_system("no_object_result",<Result>)set_system("no_object_result",<Result>)SetSystem("no_object_result",<Result>)SetSystem("no_object_result",<Result>). If necessary, an exception is raised.

Possible Predecessors

hom_mat2d_identityhom_mat2d_identityhom_mat2d_identityHomMat2dIdentityHomMat2dIdentity, hom_mat2d_translatehom_mat2d_translatehom_mat2d_translateHomMat2dTranslateHomMat2dTranslate, hom_mat2d_rotatehom_mat2d_rotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotate, hom_mat2d_scalehom_mat2d_scalehom_mat2d_scaleHomMat2dScaleHomMat2dScale

See also

affine_trans_imageaffine_trans_imageaffine_trans_imageAffineTransImageAffineTransImage, affine_trans_regionaffine_trans_regionaffine_trans_regionAffineTransRegionAffineTransRegion, affine_trans_contour_xldaffine_trans_contour_xldaffine_trans_contour_xldAffineTransContourXldAffineTransContourXld

Module

Foundation