Name
hom_mat3d_rotateT_hom_mat3d_rotateHomMat3dRotatehom_mat3d_rotateHomMat3dRotateHomMat3dRotate — Add a rotation to a homogeneous 3D transformation matrix.
void HomMat3dRotate(const HTuple& HomMat3D, const HTuple& Phi, const HTuple& Axis, const HTuple& Px, const HTuple& Py, const HTuple& Pz, HTuple* HomMat3DRotate)
HHomMat3D HHomMat3D::HomMat3dRotate(const HTuple& Phi, const HTuple& Axis, const HTuple& Px, const HTuple& Py, const HTuple& Pz) const
HHomMat3D HHomMat3D::HomMat3dRotate(double Phi, const HString& Axis, double Px, double Py, double Pz) const
HHomMat3D HHomMat3D::HomMat3dRotate(double Phi, const char* Axis, double Px, double Py, double Pz) const
void HOperatorSetX.HomMat3dRotate(
[in] VARIANT HomMat3d, [in] VARIANT Phi, [in] VARIANT Axis, [in] VARIANT Px, [in] VARIANT Py, [in] VARIANT Pz, [out] VARIANT* HomMat3dRotate)
IHHomMat3DX* HHomMat3DX.HomMat3dRotate(
[in] VARIANT Phi, [in] VARIANT Axis, [in] VARIANT Px, [in] VARIANT Py, [in] VARIANT Pz)
static void HOperatorSet.HomMat3dRotate(HTuple homMat3D, HTuple phi, HTuple axis, HTuple px, HTuple py, HTuple pz, out HTuple homMat3DRotate)
HHomMat3D HHomMat3D.HomMat3dRotate(HTuple phi, HTuple axis, HTuple px, HTuple py, HTuple pz)
HHomMat3D HHomMat3D.HomMat3dRotate(double phi, string axis, double px, double py, double pz)
hom_mat3d_rotatehom_mat3d_rotateHomMat3dRotatehom_mat3d_rotateHomMat3dRotateHomMat3dRotate adds a rotation by the angle PhiPhiPhiPhiPhiphi around the
axis passed in the parameter AxisAxisAxisAxisAxisaxis to the homogeneous 3D
transformation matrix HomMat3DHomMat3DHomMat3DHomMat3DHomMat3DhomMat3D and returns the resulting matrix in
HomMat3DRotateHomMat3DRotateHomMat3DRotateHomMat3DRotateHomMat3DRotatehomMat3DRotate. The axis can by specified by passing the strings
'x', 'y', or 'z', or by passing a vector [x,y,z] as a tuple.
The rotation is decribed by a 3×3 rotation matrix
R. It is performed relative to the global
(i.e., fixed) coordinate system; this corresponds to the following chain of
transformation matrices:
Axis = 'x':
/ 0 \ / 1 0 0 \
HomMat3DRotate = | Rx 0 | * HomMat3D Rx = | 0 cos(Phi) -sin(Phi) |
| 0 | \ 0 sin(Phi) cos(Phi) /
\ 0 0 0 1 /
Axis = 'y':
/ 0 \ / cos(Phi) 0 sin(Phi) \
HomMat3DRotate = | Ry 0 | * HomMat3D Ry = | 0 1 0 |
| 0 | \ -sin(Phi) 0 cos(Phi) /
\ 0 0 0 1 /
Axis = 'z':
/ 0 \ / cos(Phi) -sin(Phi) 0 \
HomMat3DRotate = | Rz 0 | * HomMat3D Rz = | sin(Phi) cos(Phi) 0 |
| 0 | \ 0 0 1 /
\ 0 0 0 1 /
Axis = [x,y,z]:
/ 0 \
HomMat3DRotate = | Ra 0 | * HomMat3D
| 0 |
\ 0 0 0 1 /
T T
Ra = u*u + cos(Phi)*( I-u*u ) + sin(Phi)*S
AxisAxisAxisAxisAxisaxis / x' \
u = -------- = | y' |
||AxisAxisAxisAxisAxisaxis|| \ z' /
/ 1 0 0 \ / 0 -z' y' \
I = | 0 1 0 | S = | z' 0 -x' |
\ 0 0 1 / \ -y' x' 0 /
The point (PxPxPxPxPxpx,PyPyPyPyPypy,PzPzPzPzPzpz) is the fixed point of the
transformation, i.e., this point remains unchanged when transformed using
HomMat3DRotateHomMat3DRotateHomMat3DRotateHomMat3DRotateHomMat3DRotatehomMat3DRotate. 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 rotation 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 0 +Px \ / 0 \ / 1 0 0 -Px \
HomMat3DRotate = | 0 1 0 +Py | * | R 0 | * | 0 1 0 -Py | * HomMat3D
| 0 0 1 +Pz | | 0 | | 0 0 1 -Pz |
\ 0 0 0 1 / \ 0 0 0 1 / \ 0 0 0 1 /
To perform the transformation in the local coordinate system, i.e.,
the one described by HomMat3DHomMat3DHomMat3DHomMat3DHomMat3DhomMat3D, use
hom_mat3d_rotate_localhom_mat3d_rotate_localHomMat3dRotateLocalhom_mat3d_rotate_localHomMat3dRotateLocalHomMat3dRotateLocal.
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 rc td \
| re rf rg th |
| ri rj rk tl |
\ 0 0 0 1 /
is stored as the tuple [ra, rb, rc, td, re, rf, rg, th, ri, rj, rk, tl].
However, it is also possible to process full 4×4 matrices,
which represent a projective 4D transformation.
- Multithreading type: reentrant (runs in parallel with non-exclusive operators).
- Multithreading scope: global (may be called from any thread).
- Processed without parallelization.
Input transformation matrix.
PhiPhiPhiPhiPhiphi (input_control) angle.rad → HTupleHTupleHTupleVARIANTHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong) (double / Hlong) (double / Hlong)
Rotation 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
≤
Phi
Phi
Phi
Phi
Phi
phi
≤
6.28318530718
AxisAxisAxisAxisAxisaxis (input_control) string(-array) → HTupleHTupleHTupleVARIANTHtuple (string / real / integer) (string / double / int / long) (HString / double / Hlong) (char* / double / Hlong) (BSTR / double / Hlong) (char* / double / Hlong)
Axis, to be rotated around.
Default value:
'x'
"x"
"x"
"x"
"x"
"x"
Suggested values: 'x'"x""x""x""x""x", 'y'"y""y""y""y""y", 'z'"z""z""z""z""z"
PxPxPxPxPxpx (input_control) point3d.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) point3d.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
PzPzPzPzPzpz (input_control) point3d.z → HTupleHTupleHTupleVARIANTHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong) (double / Hlong) (double / Hlong)
Fixed point of the transformation (z coordinate).
Default value: 0
Suggested values: 0, 16, 32, 64, 128, 256, 512, 1024
Output transformation matrix.
If the parameters are valid, the operator hom_mat3d_rotatehom_mat3d_rotateHomMat3dRotatehom_mat3d_rotateHomMat3dRotateHomMat3dRotate returns
2 (H_MSG_TRUE). If necessary, an exception is raised.
hom_mat3d_identityhom_mat3d_identityHomMat3dIdentityhom_mat3d_identityHomMat3dIdentityHomMat3dIdentity,
hom_mat3d_translatehom_mat3d_translateHomMat3dTranslatehom_mat3d_translateHomMat3dTranslateHomMat3dTranslate,
hom_mat3d_scalehom_mat3d_scaleHomMat3dScalehom_mat3d_scaleHomMat3dScaleHomMat3dScale,
hom_mat3d_rotatehom_mat3d_rotateHomMat3dRotatehom_mat3d_rotateHomMat3dRotateHomMat3dRotate
hom_mat3d_translatehom_mat3d_translateHomMat3dTranslatehom_mat3d_translateHomMat3dTranslateHomMat3dTranslate,
hom_mat3d_scalehom_mat3d_scaleHomMat3dScalehom_mat3d_scaleHomMat3dScaleHomMat3dScale,
hom_mat3d_rotatehom_mat3d_rotateHomMat3dRotatehom_mat3d_rotateHomMat3dRotateHomMat3dRotate
hom_mat3d_inverthom_mat3d_invertHomMat3dInverthom_mat3d_invertHomMat3dInvertHomMat3dInvert,
hom_mat3d_identityhom_mat3d_identityHomMat3dIdentityhom_mat3d_identityHomMat3dIdentityHomMat3dIdentity,
hom_mat3d_rotate_localhom_mat3d_rotate_localHomMat3dRotateLocalhom_mat3d_rotate_localHomMat3dRotateLocalHomMat3dRotateLocal,
pose_to_hom_mat3dpose_to_hom_mat3dPoseToHomMat3dpose_to_hom_mat3dPoseToHomMat3dPoseToHomMat3d,
hom_mat3d_to_posehom_mat3d_to_poseHomMat3dToPosehom_mat3d_to_poseHomMat3dToPoseHomMat3dToPose,
hom_mat3d_composehom_mat3d_composeHomMat3dComposehom_mat3d_composeHomMat3dComposeHomMat3dCompose
Foundation