Coordinate Transformation Conversion

Convert to a specified coordinate transformation representation

• Library:

• 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) – [z y x], [z y z], or [x y z]

• Homogeneous Transformation (TForm) – 4-by-4 matrix

• Quaternion (Quat) – [w x y z]

• Rotation Matrix (RotM) – 3-by-3 matrix

• Translation 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, an optional Show TrVec input/output port parameter can be selected on the block mask to toggle the multiple ports.

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) – [z y x], [z y z], or [x y z]

• Homogeneous Transformation (TForm) – 4-by-4 matrix

• Quaternion (Quat) – [w x y z]

• Rotation Matrix (RotM) – 3-by-3 matrix

• Translation 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, an optional Show TrVec input/output port parameter 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 (TForm) for the opposite transformation port to get the option to show the additional TrVec port. Enable the port by clicking Show TrVec input/output port.

Output Arguments

Output transformation — Coordinate transformation

column vector | 3-by-3 matrix | 4-by-4 matrix

Output transformation, specified as a coordinate transformation with the specified representation. The following representations are supported:

• Axis-Angle (AxAng) – [x y z theta]

• Euler Angles (Eul) – [z y x], [z y z], or [x y z]

• Homogeneous Transformation (TForm) – 4-by-4 matrix

• Quaternion (Quat) – [w x y z]

• Rotation Matrix (RotM) – 3-by-3 matrix

• Translation 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 the Homogeneous Transformation as an input or output, an optional Show TrVec input/output port parameter can be selected on the block mask to toggle the multiple ports.

TrVec — Translation vector

three-element column vector

Translation vector, specified 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 (TForm) for the opposite transformation port to get the option to show the additional TrVec port. Enable the port by clicking Show TrVec input/output port.

Parameters

Representation — Input or output representation

Axis-Angle | Euler Angles | Homogeneous Transformation | Rotation Matrix | Translation Vector | Quaternion

Select the representation for both the input and output port for the block. If you are using a transformation with only orientation information, you can also select the Show TrVec input/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 ZYX, ZYZ, or XYZ. The order of the angles in the input or output port Eul must match this rotation sequence. The default order ZYX specifies an orientation by:

• Rotating about the initial z-axis

• Rotating about the intermediate y-axis

• Rotating about the second intermediate x-axis

Dependencies

You must select Euler Angles for the Representation input or output parameter. The axis rotation sequence only applies to Euler angle rotations.

Show TrVec input/output port — Toggle TrVec port

off (default) | on

Toggle the TrVec input or output port when you want to specify or receive a separate translation vector for position information along with an orientation representation.

Dependencies

You must select Homogeneous Transformation (TForm) for the opposite transformation port to get the option to show the additional TrVec port.

Model Examples

Convert Coordinate System Transformations

How to convert some basic coordinate system transformations into other coordinate systems. Input vectors are expected to be vertical vectors.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.