This logic projects a 3D volume into 2D space. The resulting stack of 2D references can be used as references for an Alignment.

Any 3D volume can serve as input for this logic projection is performed on a HEALPIX grid or with a certain angular distance.

Projects by taking 2D slices from the Fourier transform of the 3D volume

Parameters | Description |

Padding factor | |

Euler Angle Source | Describes the source of the Euler Angles **Create**: creates grid of Euler angle combinations, **From other IO** takes angles as written in the header of a second IO, **One Angle**: a single set of angles is projected |

Sampling Mode | Sampling grid of the Euler angles. **HEALPix** uses the HEALPix algorithm, **Cylinder**: uses cylindrical coordinates |

Angular sampling | Angular distance between two sampling points |

Symmetry | Reduces the sampling grid according to point group symmetry |

Projects the 3D volume in Realspace

Parameters | Description |

Interpolation | Interpolation between the pixels |

Euler Angle Source | Describes the source of the Euler Angles **Create**: creates grid of Euler angle combinations, **From other IO** takes angles as written in the header of a second IO, **One Angle**: a single set of angles is projected |

Sampling Mode | Sampling grid of the Euler angles. **HEALPix** uses the HEALPix algorithm, **Cylinder**: uses cylindrical coordinates |

Angular sampling | Angular distance between two sampling points |

Symmetry | Reduces the sampling grid according to point group symmetry |

Input | Description |

3D | 3D volume to be projected |

*io with angles* | IO that contains the Angles to be projected |

Output | Description |

Projections | Gives stack of projections |

New/Changed Header Values | Description |

projectionId | analog of imageId for projections |

EulerAlpha | Alpha Euler Angle |

EulerBeta | Beta Euler Angle |

EulerGamma | Gamma Euler Angle |