# Volume center

The center of a discretized volume can be defined in different ways. *Dynamo* uses the same convention in all its functions. For the formulas in this page, remember also that *Dynamo* uses the convention of counting pixels with the index 1, (not 0). The pixel "on the corner" with the first coordinates in a volume `V` is thus denoted as `V[1,1,1]`.

We use the notation `[ i,j,k]` for pixel indices.

## Direct space

For a volume of `V` NxNxN pixels, *Dynamo* considers the pixel located at [N/2+1,N/2+1,N/2+1] as the center of `V`

### Rotation

Rotation needs defining on a concrete *point*, not on a pixel (as a pixel is actually a square with an area). The convention in *Dynamo* is to define the rotation center point in the middle of the center pixel

Note that the center is defined as *point*, not as a pixel.

### Placing templates in a Volume

Sometimes you need to place a template `T` inside a bigger volume `V`, by passing a pixel coordinate `r` inside the bigger volume. In such cases the placement follows by setting the central pixel [N/2+1,N/2+1,N/2+1] at the pixel position `r` in `V`, i.e.:

`
V[x-N/2 : x+N/2-1 , y-N/2 : y+N/2-1, z-N/2 : z+N/2-1] = T[:,:,:];
`