Coordinate Transformation Conversion
Convert to a specified coordinate transformation representation
Libraries:
Robotics System Toolbox /
Utilities
Navigation Toolbox /
Utilities
ROS Toolbox /
Utilities
UAV Toolbox /
Utilities
Description
The Coordinate Transformation Conversion block converts a coordinate transformation from the input representation to a specified output representation. The input and output representations use the following forms:
Axis-Angle (
AxAng
) –[x y z theta]
Euler Angles (
Eul
) – Three-element vector. For example[z y x]
.Homogeneous Transformation (
TForm
) – 4-by-4 matrixQuaternion (
Quat
) –[w x y z]
Rotation Matrix (
RotM
) – 3-by-3 matrixTranslation Vector (
TrVec
) –[x y z]
All vectors must be column vectors.
To accommodate representations that only contain position or orientation information
(TrVec
or Eul
, for example), you can specify
two inputs or outputs to handle all transformation information. When you select the
Homogeneous Transformation as an input or output, the optional Show TrVec
input port or Show TrVec output port parameters
can be selected on the block mask to toggle the multiple ports.
Examples
Convert Coordinate System Transformations
Convert some basic coordinate system transformations into other coordinate systems using Coordinate Transformation Conversion block.
Ports
Input
Input transformation — Coordinate transformation
column vector | 3-by-3 matrix | 4-by-4 matrix
Input transformation, specified as a coordinate transformation. The following representations are supported:
Axis-Angle (
AxAng
) –[x y z theta]
Euler Angles (
Eul
) – Three-element vector. For example[z y x]
.Homogeneous Transformation (
TForm
) – 4-by-4 matrixQuaternion (
Quat
) –[w x y z]
Rotation Matrix (
RotM
) – 3-by-3 matrixTranslation Vector (
TrVec
) –[x y z]
All vectors must be column vectors.
To accommodate representations that only contain position or
orientation information (TrVec
or
Eul
, for example), you can specify two inputs or
outputs to handle all transformation information. When you select the
Homogeneous Transformation as an input or output, the optional
Show TrVec input port or Show
TrVec output port parameters can be selected on the
block mask to toggle the multiple ports.
TrVec — Translation vector
3-element column vector
Translation vector, specified as a 3-element column vector,
[x y z]
, which corresponds to a translation in
the x, y, and
z axes respectively. This port can be used to
input or output the translation information separately from the rotation
vector.
Dependencies
You must select Homogeneous Transformation
for
the output Representation parameter to get
the option to show the additional TrVec input port.
Enable the port by clicking Show TrVec input
port.
Output Arguments
Output transformation — Coordinate transformation
column vector | 3-by-3 matrix | 4-by-4 matrix
Output transformation, returned as a coordinate transformation with the specified representation. The following representations are supported:
Axis-Angle (
AxAng
) –[x y z theta]
Euler Angles (
Eul
) – Three-element vector. For example[z y x]
.Homogeneous Transformation (
TForm
) – 4-by-4 matrixQuaternion (
Quat
) –[w x y z]
Rotation Matrix (
RotM
) – 3-by-3 matrixTranslation Vector (
TrVec
) –[x y z]
To accommodate representations that only contain position or
orientation information (TrVec
or
Eul
, for example), you can specify two inputs or
outputs to handle all transformation information. When you select
Homogeneous Transformation
as an input or output,
the optional Show TrVec input port or
Show TrVec output port parameters can be
selected on the block mask to toggle the multiple ports.
TrVec — Translation vector
three-element column vector
Translation vector, returned as a three-element column vector,
[x y z]
, which corresponds to a translation in
the x, y, and z
axes respectively. This port can be used to input or output the
translation information separately from the rotation vector.
Dependencies
You must select Homogeneous Transformation
for
the input Representation parameter to get the
option to show the additional TrVec output port. Enable
the port by clicking Show TrVec output
port.
Parameters
Representation — Input representation
Axis-Angle
| Euler Angles
| Homogeneous Transformation
| Quaternion
| Rotation Matrix
| Translation Vector
Select the representation for the input port for the block. If you are using a transformation with only orientation information, you can also select the Show TrVec input port or Show TrVec output port when converting to or from a homogeneous transformation.
Axis rotation sequence — Order of Euler angle axis rotations
ZYX
(default) | ZYZ
| XYZ
Order of the Euler angle axis rotations, specified as one of these string scalars:
ZYX
(default)ZYZ
ZXY
ZXZ
YXY
YZX
YXZ
YZY
XYX
XYZ
XZX
XZY
The order of the angles in the input port
Eul
must match this rotation sequence. Each
character indicates the corresponding axis. For example, if the sequence is
ZYX
, then the three specified Euler angles are
interpreted in order as a rotation around the z-axis, a
rotation around the y-axis, and a rotation around the
x-axis. When applying this rotation to a point, it
will apply the axis rotations in the order x, then
y, then z.
Dependencies
You must select Euler Angles
for the input
Representation parameter. The axis rotation
sequence only applies to Euler angle rotations.
Show TrVec input port — Toggle TrVec
port
off (default) | on
Toggle the TrVec input port when you want to specify a separate translation vector for position information along with an orientation representation.
Dependencies
You must select Homogeneous Transformation
for the
output Representation parameter to get the option
to show the additional TrVec input port. Enable the port by
clicking Show TrVec input port.
Representation — Output representation
Axis-Angle
| Euler Angles
| Homogeneous Transformation
| Quaternion
| Rotation Matrix
| Translation Vector
Select the representation for the output port for the block. If you are using a transformation with only orientation information, you can also select the Show TrVec input port or Show TrVec output port when converting to or from a homogeneous transformation.
Axis rotation sequence — Order of Euler angle axis rotations
ZYX
(default) | ZYZ
| XYZ
Order of the Euler angle axis rotations, specified as one of these string scalars:
ZYX
(default)ZYZ
ZXY
ZXZ
YXY
YZX
YXZ
YZY
XYX
XYZ
XZX
XZY
The order of the angles in the output port
Eul
must match this rotation sequence. Each
character indicates the corresponding axis. For example, if the sequence is
ZYX
, then the three returned Euler angles are
interpreted in order as a rotation around the z-axis, a
rotation around the y-axis, and a rotation around the
x-axis. When applying this rotation to a point, it
will apply the axis rotations in the order x, then
y, then z.
Dependencies
You must select Euler Angles
for the output
Representation parameter. The axis rotation
sequence only applies to Euler angle rotations.
Show TrVec output port — Toggle TrVec
port
off (default) | on
Toggle the TrVec output port when you want to receive a separate translation vector for position information along with an orientation representation.
Dependencies
You must select Homogeneous Transformation
for the
input Representation parameter to get the option
to show the additional TrVec output port. Enable the port
by clicking Show TrVec output port.
Simulate using — Type of simulation to run
Interpreted execution
(default) | Code generation
Interpreted execution
— Simulate model using the MATLAB® interpreter. This option shortens startup time but has a slower simulation speed thanCode generation
. In this mode, you can debug the source code of the block.Code generation
— Simulate model using generated C code. The first time you run a simulation, Simulink® generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change. This option requires additional startup time, but the speed of the subsequent simulations is comparable toInterpreted execution
.
Tunable: No
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced in R2017bR2024b: Additional Euler sequence support
The Coordinate Transformation Conversion block supports additional Euler sequences for the Axis rotation sequence parameter. These are all the supported Euler sequences:
ZYX
ZYZ
ZXY
ZXZ
YXY
YZX
YXZ
YZY
XYX
XYZ
XZX
XZY
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