Engee documentation

Coordinate Transformation Conversion

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Conversion to a given coordinate representation.

blockType: CoordinateTransformationConversion

coordinate transformation conversion

Path in the library:

/Navigation/Utilities/Coordinate Transformation Conversion

Description

Block Coordinate Transformation Conversion converts coordinates from an input representation to a specified output representation. The input and output representations have the following forms:

  • Axis-Angle — the angle between the axes (AxAng) — [x y z theta];

  • Euler Angles — Euler angles (Eul) — a three-element vector, for example [z y x];

  • Homogeneous Transformation — homogeneous transformation (TForm) — matrix 4 on 4;

  • Quaternion — Quaternion (Quat) — [w x y z];

  • Rotation Matrix — rotation matrix (RotM) — matrix 3 on 3;

  • Translation Vector — displacement vector (TrVec) — [x y z].

All vectors must be vectors-column.

To process representations containing only position or orientation information (for example, TrVec or Eul), you can specify two Inputs or outputs to process all transformation information. When selecting a homogeneous transformation as an Input or output, optional checkboxes can be set on the block mask Show TrVec input port or Show TrVec output port to switch between multiple ports.

Ports

Input

# Input transformation — coordinate conversion
column vector | the matrix is 3 by 3 | the matrix is 4 by 4

Details

The input transformation specified as the coordinate transformation. The following views are supported:

  • The angle between the axes (AxAng) — [x y z theta];

  • Euler angles (Eul) is a three—element vector, for example [z y x];

  • Homogeneous transformation (TForm) — matrix 4 on 4;

  • Quaternion (Quat, by default) — [w x y z];

  • The rotation matrix (RotM) is a matrix 3 on 3;

  • Displacement vector (TrVec) — [x y z].

All vectors must be vectors-column.

To process views that contain only position or orientation information (for example, TrVec or Eul), you can specify two Inputs or outputs to process all transformation information. When selecting a homogeneous transformation as an Input or output, optional checkboxes can be set on the block mask Show TrVec input port or Show TrVec output port to switch between multiple ports.

Data types

Float64, Float32
Complex numbers support

Yes

# TrVec — displacement vector
three-element column vector

Details

The displacement vector specified as a three-element column vector [x y z] corresponding to the axis offset , and accordingly. This port can be used to input or output movement information separately from the rotation vector.

Dependencies

To use this port, set the parameter Representation value Homogeneous Transformation and check the box Show TrVec input port.

Data types

Float64, Float32
Complex numbers support

Yes

Output

# Output transformation — coordinate transformation
column vector | the matrix is 3 by 3 | the matrix is 4 by 4

Details

The output transformation returned as a coordinate transformation with the specified representation. The following views are supported:

  • The angle between the axes (AxAng) — [x y z theta];

  • Euler angles (Eul) is a three—element vector, for example [z y x];

  • Homogeneous transformation (TForm) — matrix 4 on 4;

  • Quaternion (Quat) — [w x y z].

  • Rotation matrix (RotM, by default) — matrix 3 on 3;

  • Displacement vector (TrVec) — [x y z].

All vectors must be vectors-column.

To process representations containing only position or orientation information (for example, TrVec or Eul), you can specify two Inputs or outputs to process all transformation information. When selecting a homogeneous transformation as an Input or output, optional checkboxes can be set on the block mask Show TrVec input port or Show TrVec output port to switch between multiple ports.

Data types

Float64, Float32
Complex numbers support

Yes

# TrVec — displacement vector

+ three-element column vector

Details

The displacement vector returned as a three-element column vector [x y z], corresponding to the offset along the axes , and accordingly. This port can be used to input or output movement information separately from the rotation vector.

Dependencies

To use this port, set the parameter Representation value Homogeneous Transformation and check the box Show TrVec output port.

Типы данных

Float64, Float32
Support for complex numbers

Yes

Parameters

Input

# Representation — The input representation
Axis-Angle | Euler Angles | Homogeneous Transformation | Quaternion | Rotation Matrix | Translation Vector

Details

Select the representation for the input port of the block. If you are using a transformation that contains orientation information only, you can also check the boxes Show TrVec input port or Show TrVec output port when converting to or from a homogeneous transformation.

Values

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

Quaternion
Program usage name

InputRepresentation
Tunable

No
Evaluatable

No

# Axis rotation sequence — the order of rotations of the axis of Euler angles
ZYX | ZYZ | XYZ | ZXY | ZXZ | YXZ | YXY | YZX | YZY | XYX | XZY | XZX

Details

The order of rotations of the axis of the Euler angles, given by one of the following scalar values:

  • ZYX (by default);

  • ZYZ;

  • XYZ;

  • ZXY;

  • ZXZ;

  • YXZ;

  • YXY;

  • YZX;

  • YZY;

  • XYX;

  • XZY;

  • XZX.

The order of the corners in the input port Eul must correspond to this sequence of turns. Each symbol represents a corresponding axis. For example, if the sequence — ZYX, then the three given Euler angles are interpreted in order as rotations around the axis , rotation around the axis and rotation around the axis . When applying this rotation to a point, the axis rotation will be applied in the following order , then , then .

Dependencies

To use this parameter, set for the input parameter Representation meaning Euler Angles. The rotation sequence around the axes applies only to rotations around Euler angles.

Values

ZYX | ZYZ | XYZ | ZXY | ZXZ | YXZ | YXY | YZX | YZY | XYX | XZY | XZX
Default value

ZYX
Program usage name

InputEulerSequence
Tunable

No
Evaluatable

No

# Show TrVec input port — enable the TrVec input port
Logical

Details

Enable the TrVec input port if you want to specify a separate displacement vector for position information along with an orientation representation.

Dependencies

To use this parameter, set for the input parameter Representation meaning Homogeneous Transformation. Enable the TrVec port by checking the box Show TrVec input port.

Default value

false (switched off)
Program usage name

ShowTrVecInputPort
Tunable

No
Evaluatable

No

Output

# Representation — output representation
Axis-Angle | Euler Angles | Homogeneous Transformation | Quaternion | Rotation Matrix | Translation Vector

Details

Select the representation for the output port of the block. If you are using a transformation that contains orientation information only, you can also check the boxes Show TrVec input port or Show TrVec output port when converting to or from a homogeneous transformation.

Values

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

Rotation Matrix
Program usage name

OutputRepresentation
Tunable

No
Evaluatable

No

# Axis rotation sequence — the order of rotations of the axis of Euler angles
ZYX | ZYZ | XYZ | ZXY | ZXZ | YXZ | YXY | YZX | YZY | XYX | XZY | XZX

Details

The order of rotations of the axis of the Euler angles, given by one of the following scalar values:

  • ZYX (by default);

  • ZYZ;

  • XYZ;

  • ZXY;

  • ZXZ;

  • YXZ;

  • YXY;

  • YZX;

  • YZY;

  • XYX;

  • XZY;

  • XZX.

The order of the angles in the output port Eul must correspond to this sequence of turns. Each symbol represents a corresponding axis. For example, if the sequence — ZYX, then the three returned Euler angles are interpreted in order as rotations around the axis , rotation around the axis and rotation around the axis . When applying this rotation to a point, the axis rotation will be applied in the following order , then , then .

Dependencies

To use this parameter, set for the output parameter Representation meaning Euler Angles. The rotation sequence around the axes applies only to rotations around Euler angles.

Values

ZYX | ZYZ | XYZ | ZXY | ZXZ | YXZ | YXY | YZX | YZY | XYX | XZY | XZX
Default value

ZYX
Program usage name

OutputEulerSequence
Tunable

No
Evaluatable

No

# Show TrVec output port — enable the TrVec output port
Logical

Details

Turn on the TrVec output port if you want to receive a separate displacement vector for position information along with an orientation representation.

Dependencies

To use this parameter, set for the output parameter Representation meaning Homogeneous Transformation. Enable the TrVec port by checking the box Show TrVec output port.

Default value

false (switched off)
Program usage name

ShowTrVecOutputPort
Tunable

No
Evaluatable

No