# 2D Geometries¶

## Volume Geometries¶

Create a 2D volume geometry:

```vol_geom = astra_create_vol_geom(rows_and_cols);
vol_geom = astra_create_vol_geom([rows cols]);
vol_geom = astra_create_vol_geom(rows, cols);
vol_geom = astra_create_vol_geom(rows, cols, min_x, max_x, min_y, max_y);
```

In the first form, the volume contains an equal number of rows and columns. In the first, second and third forms, volume pixels are squares with sides of unit length, and the volume is centered around the origin. In the fourth, longer form, the extents of the volume can be specified arbitrarily. The long form corresponding to the default short form is:

```vol_geom = astra_create_vol_geom(y, x, -x/2, x/2, -y/2, y/2);
```

Note: For usage with GPU code, the volume must be centered around the origin and pixels must be square. This is not always explicitly checked in all functions, so not following these requirements may have unpredictable results.

## Projection Geometries¶

parallel

Create a 2D parallel beam geometry:

```proj_geom = astra_create_proj_geom('parallel', det_width, det_count, angles);
```
• det_spacing: distance between the centers of two adjacent detector pixels

• det_count: number of detector pixels in a single projection

• angles: projection angles in radians

fanflat

Create a 2D flat fan beam geometry:

```proj_geom = astra_create_proj_geom('fanflat', det_width, det_count, angles, source_origin, origin_det);
```
• det_width: distance between the centers of two adjacent detector pixels

• det_count: number of detector pixels in a single projection

• angles: projection angles in radians

• source_origin: distance between the source and the center of rotation

• origin_det: distance between the center of rotation and the detector array

fanflat_vec

Create a 2D flat fan beam geometry specified by 2D vectors:

```proj_geom = astra_create_proj_geom('fanflat_vec', det_count, vectors);
```
• det_count: number of detectors in a single projection

• vectors: a matrix containing the actual geometry. Each row of vectors corresponds to a single projection, and consists of: ( srcX, srcY, dX, dY, uX, uY )

• src : the ray source

• d : the center of the detector

• u : the vector between the centers of detector pixels 0 and 1

To illustrate, this is a matlab script to convert a single projection in a projection geometry of type “fanflat” into such a 6-element row:

```% source
vectors(i,1) = sin(proj_geom.ProjectionAngles(i)) * proj_geom.DistanceOriginSource;
vectors(i,2) = -cos(proj_geom.ProjectionAngles(i)) * proj_geom.DistanceOriginSource;

% center of detector
vectors(i,3) = -sin(proj_geom.ProjectionAngles(i)) * proj_geom.DistanceOriginDetector;
vectors(i,4) = cos(proj_geom.ProjectionAngles(i)) * proj_geom.DistanceOriginDetector;

% vector from detector pixel 0 to 1
vectors(i,5) = cos(proj_geom.ProjectionAngles(i)) * proj_geom.DetectorWidth;
vectors(i,6) = sin(proj_geom.ProjectionAngles(i)) * proj_geom.DetectorWidth;
```

This conversion is also available as a function in the toolbox:

```proj_geom_vec = astra_geom_2vec(proj_geom);
```

sparse_matrix

Create a 2D projection geometry defined by its system matrix:

```proj_geom = astra_create_proj_geom('sparse_matrix', det_width, det_count, angles, matrix_id);
```
• det_width: unused, but has to be present (for compatibility reasons)

• det_count: number of detectors in a single projection

• angles: a vector, the length of which is the number of projections. The contents are unused.

• matrix_id: a astra_mex_matrix ID of a sparse matrix of the right dimensions.

The matrix is an ID returned by

```matrix_id = astra_mex_matrix('create', matlab_sparse_matrix);
```

The sparse matrix must be of size (det_count * numel(angles), x*y), where (x,y) is the size of the volume geometry to be used.

The rows of the sparse matrix are ordered by projection: The first row of the matrix corresponds to the first detector pixel of the first projection, and the second row of the matrix corresponds to the second detector pixel of the first projection.

The columns of the sparse matrix are ordered by row: The first column of the matrix corresponds to pixel (1,1) and the second column to pixel (1,2) in the volume.