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hom_mat2d_reflectT_hom_mat2d_reflectHomMat2dReflecthom_mat2d_reflectHomMat2dReflectHomMat2dReflect (Operator)

Name

hom_mat2d_reflectT_hom_mat2d_reflectHomMat2dReflecthom_mat2d_reflectHomMat2dReflectHomMat2dReflect — Add a reflection to a homogeneous 2D transformation matrix.

Signature

hom_mat2d_reflect( : : HomMat2D, Px, Py, Qx, Qy : HomMat2DReflect)

Herror T_hom_mat2d_reflect(const Htuple HomMat2D, const Htuple Px, const Htuple Py, const Htuple Qx, const Htuple Qy, Htuple* HomMat2DReflect)

Herror hom_mat2d_reflect(const HTuple& HomMat2D, const HTuple& Px, const HTuple& Py, const HTuple& Qx, const HTuple& Qy, HTuple* HomMat2DReflect)

void HomMat2dReflect(const HTuple& HomMat2D, const HTuple& Px, const HTuple& Py, const HTuple& Qx, const HTuple& Qy, HTuple* HomMat2DReflect)

HHomMat2D HHomMat2D::HomMat2dReflect(const HTuple& Px, const HTuple& Py, const HTuple& Qx, const HTuple& Qy) const

HHomMat2D HHomMat2D::HomMat2dReflect(double Px, double Py, double Qx, double Qy) const

void HOperatorSetX.HomMat2dReflect(
[in] VARIANT HomMat2d, [in] VARIANT Px, [in] VARIANT Py, [in] VARIANT Qx, [in] VARIANT Qy, [out] VARIANT* HomMat2dReflect)

IHHomMat2DX* HHomMat2DX.HomMat2dReflect(
[in] VARIANT Px, [in] VARIANT Py, [in] VARIANT Qx, [in] VARIANT Qy)

static void HOperatorSet.HomMat2dReflect(HTuple homMat2D, HTuple px, HTuple py, HTuple qx, HTuple qy, out HTuple homMat2DReflect)

HHomMat2D HHomMat2D.HomMat2dReflect(HTuple px, HTuple py, HTuple qx, HTuple qy)

HHomMat2D HHomMat2D.HomMat2dReflect(double px, double py, double qx, double qy)

Description

hom_mat2d_reflecthom_mat2d_reflectHomMat2dReflecthom_mat2d_reflectHomMat2dReflectHomMat2dReflect adds a reflection about the axis given by the two points (PxPxPxPxPxpx,PyPyPyPyPypy) and (QxQxQxQxQxqx,QyQyQyQyQyqy) to the homogeneous 2D transformation matrix HomMat2DHomMat2DHomMat2DHomMat2DHomMat2DhomMat2D and returns the resulting matrix in HomMat2DReflectHomMat2DReflectHomMat2DReflectHomMat2DReflectHomMat2DReflecthomMat2DReflect. The reflection is described by a 2×2 reflection matrix M. It is performed relative to the global (i.e., fixed) coordinate system; this corresponds to the following chain of transformation matrices:

                    / Mxx Mxy 0 \
  HomMat2DReflect = | Mxy Myy 0 | * HomMat2D
                    \ 0   0   1 /

                              2      T
       M = | Mxx Mxy | = I - ---- v*v
           | Mxy Myy |        T
                             v *v

                         T
  where v = (Py-Qy,Qx-Px)  is the normal vector to the axis.

The axis (PxPxPxPxPxpx,PyPyPyPyPypy)-(QxQxQxQxQxqx,QyQyQyQyQyqy) is fixed in the transformation, i.e., the points on the axis remain unchanged when transformed using HomMat2DReflectHomMat2DReflectHomMat2DReflectHomMat2DReflectHomMat2DReflecthomMat2DReflect. To obtain this behavior, first a translation is added to the input transformation matrix that moves the axis onto the origin of the global coordinate system. Then, the reflection is added, and finally a translation that moves the axis back to its original position. This corresponds to the following chain of transformations:

                    / 1 0 +Px \   / Mxx Mxy 0 \   / 1 0 -Px \
  HomMat2DReflect = | 0 1 +Py | * | Mxy Myy 0 | * | 0 1 -Py | * HomMat2D
                    \ 0 0  1  /   \ 0   0   1 /   \ 0 0  1  /

To perform the transformation in the local coordinate system, i.e., the one described by HomMat2DHomMat2DHomMat2DHomMat2DHomMat2DhomMat2D, use hom_mat2d_reflect_localhom_mat2d_reflect_localHomMat2dReflectLocalhom_mat2d_reflect_localHomMat2dReflectLocalHomMat2dReflectLocal.

Attention

It should be noted that homogeneous transformation matrices refer to a general right-handed mathematical coordinate system. If a homogeneous transformation matrix is used to transform images, regions, XLD contours, or any other data that has been extracted from images, the row coordinates of the transformation must be passed in the x coordinates, while the column coordinates must be passed in the y coordinates. Consequently, the order of passing row and column coordinates follows the usual order (RowRowRowRowRowrow,ColumnColumnColumnColumnColumncolumn). This convention is essential to obtain a right-handed coordinate system for the transformation of iconic data, and consequently to ensure in particular that rotations are performed in the correct mathematical direction.

Note that homogeneous matrices are stored row-by-row as a tuple; the last row is usually not stored because it is identical for all homogeneous matrices that describe an affine transformation. For example, the homogeneous matrix

    / ra rb tc \
    | rd re tf |
    \ 0  0  1  /

is stored as the tuple [ra, rb, tc, rd, re, tf]. However, it is also possible to process full 3×3 matrices, which represent a projective 2D transformation.

Parallelization

Parameters

HomMat2DHomMat2DHomMat2DHomMat2DHomMat2DhomMat2D (input_control)  hom_mat2d HHomMat2D, HTupleHTupleHTupleHHomMat2DX, VARIANTHtuple (real) (double) (double) (double) (double) (double)

Input transformation matrix.

PxPxPxPxPxpx (input_control)  point.x HTupleHTupleHTupleVARIANTHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong) (double / Hlong) (double / Hlong)

First point of the axis (x coordinate).

Default value: 0

Suggested values: 0, 16, 32, 64, 128, 256, 512, 1024

PyPyPyPyPypy (input_control)  point.y HTupleHTupleHTupleVARIANTHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong) (double / Hlong) (double / Hlong)

First point of the axis (y coordinate).

Default value: 0

Suggested values: 0, 16, 32, 64, 128, 256, 512, 1024

QxQxQxQxQxqx (input_control)  point.x HTupleHTupleHTupleVARIANTHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong) (double / Hlong) (double / Hlong)

Second point of the axis (x coordinate).

Default value: 16

Suggested values: 0, 16, 32, 64, 128, 256, 512, 1024

QyQyQyQyQyqy (input_control)  point.y HTupleHTupleHTupleVARIANTHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong) (double / Hlong) (double / Hlong)

Second point of the axis (y coordinate).

Default value: 32

Suggested values: 0, 16, 32, 64, 128, 256, 512, 1024

HomMat2DReflectHomMat2DReflectHomMat2DReflectHomMat2DReflectHomMat2DReflecthomMat2DReflect (output_control)  hom_mat2d HHomMat2D, HTupleHTupleHTupleHHomMat2DX, VARIANTHtuple (real) (double) (double) (double) (double) (double)

Output transformation matrix.

Result

hom_mat2d_reflecthom_mat2d_reflectHomMat2dReflecthom_mat2d_reflectHomMat2dReflectHomMat2dReflect returns 2 (H_MSG_TRUE) if both points on the axis are not identical. If necessary, an exception is raised.

Possible Predecessors

hom_mat2d_identityhom_mat2d_identityHomMat2dIdentityhom_mat2d_identityHomMat2dIdentityHomMat2dIdentity, hom_mat2d_translatehom_mat2d_translateHomMat2dTranslatehom_mat2d_translateHomMat2dTranslateHomMat2dTranslate, hom_mat2d_scalehom_mat2d_scaleHomMat2dScalehom_mat2d_scaleHomMat2dScaleHomMat2dScale, hom_mat2d_rotatehom_mat2d_rotateHomMat2dRotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotate, hom_mat2d_slanthom_mat2d_slantHomMat2dSlanthom_mat2d_slantHomMat2dSlantHomMat2dSlant, hom_mat2d_reflecthom_mat2d_reflectHomMat2dReflecthom_mat2d_reflectHomMat2dReflectHomMat2dReflect

Possible Successors

hom_mat2d_translatehom_mat2d_translateHomMat2dTranslatehom_mat2d_translateHomMat2dTranslateHomMat2dTranslate, hom_mat2d_scalehom_mat2d_scaleHomMat2dScalehom_mat2d_scaleHomMat2dScaleHomMat2dScale, hom_mat2d_rotatehom_mat2d_rotateHomMat2dRotatehom_mat2d_rotateHomMat2dRotateHomMat2dRotate, hom_mat2d_slanthom_mat2d_slantHomMat2dSlanthom_mat2d_slantHomMat2dSlantHomMat2dSlant, hom_mat2d_reflecthom_mat2d_reflectHomMat2dReflecthom_mat2d_reflectHomMat2dReflectHomMat2dReflect

See also

hom_mat2d_reflect_localhom_mat2d_reflect_localHomMat2dReflectLocalhom_mat2d_reflect_localHomMat2dReflectLocalHomMat2dReflectLocal

Module

Foundation


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