====== Projection ======
This logic projects a 3D volume into 2D space. The resulting stack of 2D references can be used as references for an [[eyes:logics:alignment|]]. 

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

===== Mode =====
==== Fourier ====
Projects by taking 2D slices from the Fourier transform of the 3D volume 
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^ Parameters                 ^ Description     ^
| Padding factor  | FIXME |
| 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|

==== Real Space ====
Projects the 3D volume in Realspace
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^ 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|


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^ Input   ^ Description ^
| 3D  | 3D volume to be projected |
| //io with angles//  | IO that contains the Angles to be projected  |

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^ Output   ^ Description ^
| Projections | Gives stack of projections |

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^ New/Changed Header Values ^ Description ^
| projectionId | analog of imageId for projections |
| EulerAlpha | Alpha Euler Angle |
| EulerBeta | Beta Euler Angle |
| EulerGamma | Gamma Euler Angle |