# Transform

A similarity transform is a geometric transformation in which an object is scaled, rotated, and translated, preserving its shape. It is a combination of a scaling, rotation, and translation, and can be represented by a single matrix. The similarity transform preserves the ratios of distances between points and the angles between lines in the original object.

## Outputs

#### T(x)

Resulting transform.

Type: Struct

## Settings

### Configure

#### Extrapolation Value Number

The default voxel value for voxels outside the Frame of Reference.

#### New Frame of Reference Boolean

The Frame of Reference describes the position, orientation, matrix size, and voxel size, of the transformed input.

#### Initial Transform Boolean

Add an initial transform to the output.

### Rotation

#### Rotational Representation Selection

Select input rotation representation.

Rotation Axis and Angle describes a rotation around an axis defined by a vector. The input vector does not have to be normalized. This is the default representation.

Rotation Matrix describes the rotation as a 3x3 orthogonal matrix. The rotation matrix must have a determinant of 1.

Euler Angles describes intrinsic rotation around three principal axes X, Y, Z, which can be described as yaw, pitch, and roll. Intrinsic rotation means that the rotations occur about the axes of a coordinate system that is attached to the moving body. The order in which the rotations are applied is important. Two options are available: ZXY and ZYX.

Values: Rotation Axis and Angle, Rotation Matrix, Euler Angles (ZXY), Euler Angles (ZYX)

#### Rotational Axis 3D Vector

The axis of rotation, described as a vector. The input does not have to be normalized.

The rotation in radians around the axis of rotation.

#### Rotation Matrix Array

The matrix must be orthogonal with a determinant of 1.

Set the rotation as described by Euler angles around X, Y and Z.

#### Center Of Rotation [mm] Numbers

The coordinate around which the rotation is defined.

### Parameters

#### Translation [mm] Numbers

The translation vector of the transform.

#### Uniform Scale Number

The uniform scaling of the transform.