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hom_mat2d_scaleT_hom_mat2d_scaleHomMat2dScalehom_mat2d_scaleHomMat2dScaleHomMat2dScale (Operator)

Name

hom_mat2d_scaleT_hom_mat2d_scaleHomMat2dScalehom_mat2d_scaleHomMat2dScaleHomMat2dScale — Add a scaling to a homogeneous 2D transformation matrix.

Signature

hom_mat2d_scale( : : HomMat2D, Sx, Sy, Px, Py : HomMat2DScale)

Herror T_hom_mat2d_scale(const Htuple HomMat2D, const Htuple Sx, const Htuple Sy, const Htuple Px, const Htuple Py, Htuple* HomMat2DScale)

Herror hom_mat2d_scale(const HTuple& HomMat2D, const HTuple& Sx, const HTuple& Sy, const HTuple& Px, const HTuple& Py, HTuple* HomMat2DScale)

void HomMat2dScale(const HTuple& HomMat2D, const HTuple& Sx, const HTuple& Sy, const HTuple& Px, const HTuple& Py, HTuple* HomMat2DScale)

HHomMat2D HHomMat2D::HomMat2dScale(const HTuple& Sx, const HTuple& Sy, const HTuple& Px, const HTuple& Py) const

HHomMat2D HHomMat2D::HomMat2dScale(double Sx, double Sy, double Px, double Py) const

void HOperatorSetX.HomMat2dScale(
[in] VARIANT HomMat2d, [in] VARIANT Sx, [in] VARIANT Sy, [in] VARIANT Px, [in] VARIANT Py, [out] VARIANT* HomMat2dScale)

IHHomMat2DX* HHomMat2DX.HomMat2dScale(
[in] VARIANT Sx, [in] VARIANT Sy, [in] VARIANT Px, [in] VARIANT Py)

static void HOperatorSet.HomMat2dScale(HTuple homMat2D, HTuple sx, HTuple sy, HTuple px, HTuple py, out HTuple homMat2DScale)

HHomMat2D HHomMat2D.HomMat2dScale(HTuple sx, HTuple sy, HTuple px, HTuple py)

HHomMat2D HHomMat2D.HomMat2dScale(double sx, double sy, double px, double py)

Description

hom_mat2d_scalehom_mat2d_scaleHomMat2dScalehom_mat2d_scaleHomMat2dScaleHomMat2dScale adds a scaling by the scale factors SxSxSxSxSxsx and SySySySySysy to the homogeneous 2D transformation matrix HomMat2DHomMat2DHomMat2DHomMat2DHomMat2DhomMat2D and returns the resulting matrix in HomMat2DScaleHomMat2DScaleHomMat2DScaleHomMat2DScaleHomMat2DScalehomMat2DScale. The scaling is described by a 2×2 scaling matrix S. It is performed relative to the global (i.e., fixed) coordinate system; this corresponds to the following chain of transformation matrices:

                  / Sx 0  0 \
  HomMat2DScale = | 0  Sy 0 | * HomMat2D
                  \ 0  0  1 /

       S = | Sx 0 |
           | 0 Sy |

The point (PxPxPxPxPxpx,PyPyPyPyPypy) is the fixed point of the transformation, i.e., this point remains unchanged when transformed using HomMat2DScaleHomMat2DScaleHomMat2DScaleHomMat2DScaleHomMat2DScalehomMat2DScale. To obtain this behavior, first a translation is added to the input transformation matrix that moves the fixed point onto the origin of the global coordinate system. Then, the scaling is added, and finally a translation that moves the fixed point back to its original position. This corresponds to the following chain of transformations:

                  / 1 0 +Px \   / Sx 0  0 \   / 1 0 -Px \
  HomMat2DScale = | 0 1 +Py | * | 0  Sy 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_scale_localhom_mat2d_scale_localHomMat2dScaleLocalhom_mat2d_scale_localHomMat2dScaleLocalHomMat2dScaleLocal.

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.

SxSxSxSxSxsx (input_control)  number HTupleHTupleHTupleVARIANTHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong) (double / Hlong) (double / Hlong)

Scale factor along the x-axis.

Default value: 2

Suggested values: 0.125, 0.25, 0.5, 1, 2, 4, 8, 16

Restriction: Sx != 0

SySySySySysy (input_control)  number HTupleHTupleHTupleVARIANTHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong) (double / Hlong) (double / Hlong)

Scale factor along the y-axis.

Default value: 2

Suggested values: 0.125, 0.25, 0.5, 1, 2, 4, 8, 16

Restriction: Sy != 0

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

Fixed point of the transformation (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)

Fixed point of the transformation (y coordinate).

Default value: 0

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

HomMat2DScaleHomMat2DScaleHomMat2DScaleHomMat2DScaleHomMat2DScalehomMat2DScale (output_control)  hom_mat2d HHomMat2D, HTupleHTupleHTupleHHomMat2DX, VARIANTHtuple (real) (double) (double) (double) (double) (double)

Output transformation matrix.

Result

hom_mat2d_scalehom_mat2d_scaleHomMat2dScalehom_mat2d_scaleHomMat2dScaleHomMat2dScale returns 2 (H_MSG_TRUE) if both scale factors are not 0. 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_scale_localhom_mat2d_scale_localHomMat2dScaleLocalhom_mat2d_scale_localHomMat2dScaleLocalHomMat2dScaleLocal

Module

Foundation


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