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hom_mat2d_slantT_hom_mat2d_slantHomMat2dSlanthom_mat2d_slantHomMat2dSlantHomMat2dSlant (Operator)

Name

hom_mat2d_slantT_hom_mat2d_slantHomMat2dSlanthom_mat2d_slantHomMat2dSlantHomMat2dSlant — Add a slant to a homogeneous 2D transformation matrix.

Signature

hom_mat2d_slant( : : HomMat2D, Theta, Axis, Px, Py : HomMat2DSlant)

Herror T_hom_mat2d_slant(const Htuple HomMat2D, const Htuple Theta, const Htuple Axis, const Htuple Px, const Htuple Py, Htuple* HomMat2DSlant)

Herror hom_mat2d_slant(const HTuple& HomMat2D, const HTuple& Theta, const HTuple& Axis, const HTuple& Px, const HTuple& Py, HTuple* HomMat2DSlant)

void HomMat2dSlant(const HTuple& HomMat2D, const HTuple& Theta, const HTuple& Axis, const HTuple& Px, const HTuple& Py, HTuple* HomMat2DSlant)

HHomMat2D HHomMat2D::HomMat2dSlant(const HTuple& Theta, const HString& Axis, const HTuple& Px, const HTuple& Py) const

HHomMat2D HHomMat2D::HomMat2dSlant(double Theta, const HString& Axis, double Px, double Py) const

HHomMat2D HHomMat2D::HomMat2dSlant(double Theta, const char* Axis, double Px, double Py) const

void HOperatorSetX.HomMat2dSlant(
[in] VARIANT HomMat2d, [in] VARIANT Theta, [in] VARIANT Axis, [in] VARIANT Px, [in] VARIANT Py, [out] VARIANT* HomMat2dSlant)

IHHomMat2DX* HHomMat2DX.HomMat2dSlant(
[in] VARIANT Theta, [in] BSTR Axis, [in] VARIANT Px, [in] VARIANT Py)

static void HOperatorSet.HomMat2dSlant(HTuple homMat2D, HTuple theta, HTuple axis, HTuple px, HTuple py, out HTuple homMat2DSlant)

HHomMat2D HHomMat2D.HomMat2dSlant(HTuple theta, string axis, HTuple px, HTuple py)

HHomMat2D HHomMat2D.HomMat2dSlant(double theta, string axis, double px, double py)

Description

hom_mat2d_slanthom_mat2d_slantHomMat2dSlanthom_mat2d_slantHomMat2dSlantHomMat2dSlant adds a slant by the angle ThetaThetaThetaThetaThetatheta to the homogeneous 2D transformation matrix HomMat2DHomMat2DHomMat2DHomMat2DHomMat2DhomMat2D and returns the resulting matrix in HomMat2DSlantHomMat2DSlantHomMat2DSlantHomMat2DSlantHomMat2DSlanthomMat2DSlant. A slant is an affine transformation in which one coordinate axis remains fixed, while the other coordinate axis is rotated counterclockwise by an angle ThetaThetaThetaThetaThetatheta. The parameter AxisAxisAxisAxisAxisaxis determines which coordinate axis is slanted. For AxisAxisAxisAxisAxisaxis = 'x'"x""x""x""x""x", the x-axis is slanted and the y-axis remains fixed, while for AxisAxisAxisAxisAxisaxis = 'y'"y""y""y""y""y" the y-axis is slanted and the x-axis remains fixed. The slanting is performed relative to the global (i.e., fixed) coordinate system; this corresponds to the following chains of transformation matrices:

                               / cos(Theta) 0 0 \
  Axis = 'x':  HomMat2DSlant = | sin(Theta) 1 0 | * HomMat2D
                               \    0       0 1 /

                               / 1 -sin(Theta) 0 \
  Axis = 'y':  HomMat2DSlant = | 0  cos(Theta) 0 | * HomMat2D
                               \ 0     0       1 /

The point (PxPxPxPxPxpx,PyPyPyPyPypy) is the fixed point of the transformation, i.e., this point remains unchanged when transformed using HomMat2DSlantHomMat2DSlantHomMat2DSlantHomMat2DSlantHomMat2DSlanthomMat2DSlant. 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 slant is added, and finally a translation that moves the fixed point back to its original position. This corresponds to the following chain of transformations for AxisAxisAxisAxisAxisaxis = 'x'"x""x""x""x""x":

                  / 1 0 +Px \   / cos(Theta) 0 0 \   / 1 0 -Px \
  HomMat2DSlant = | 0 1 +Py | * | sin(Theta) 1 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_slant_localhom_mat2d_slant_localHomMat2dSlantLocalhom_mat2d_slant_localHomMat2dSlantLocalHomMat2dSlantLocal.

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.

ThetaThetaThetaThetaThetatheta (input_control)  angle.rad HTupleHTupleHTupleVARIANTHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong) (double / Hlong) (double / Hlong)

Slant angle.

Default value: 0.78

Suggested values: 0.1, 0.2, 0.3, 0.4, 0.78, 1.57, 3.14

Typical range of values: 0 ≤ Theta Theta Theta Theta Theta theta ≤ 6.28318530718

AxisAxisAxisAxisAxisaxis (input_control)  string HTupleHTupleHTupleVARIANTHtuple (string) (string) (HString) (char*) (BSTR) (char*)

Coordinate axis that is slanted.

Default value: 'x' "x" "x" "x" "x" "x"

List of values: 'x'"x""x""x""x""x", 'y'"y""y""y""y""y"

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

HomMat2DSlantHomMat2DSlantHomMat2DSlantHomMat2DSlantHomMat2DSlanthomMat2DSlant (output_control)  hom_mat2d HHomMat2D, HTupleHTupleHTupleHHomMat2DX, VARIANTHtuple (real) (double) (double) (double) (double) (double)

Output transformation matrix.

Result

If the parameters are valid, the operator hom_mat2d_slanthom_mat2d_slantHomMat2dSlanthom_mat2d_slantHomMat2dSlantHomMat2dSlant returns 2 (H_MSG_TRUE). 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_slant_localhom_mat2d_slant_localHomMat2dSlantLocalhom_mat2d_slant_localHomMat2dSlantLocalHomMat2dSlantLocal

Module

Foundation


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