How to see if a template polygon with dimensions will fit inside of a parcel polygon?

This may be possible in FME, following an algorithm like this:

1. Create a point grid inside the parcels
2. Move a copy of each site template to every grid point (put the center of the site template on the grid point)
3. Create copies of these copies, and rotate each copy with a different rotation angle around its center point
4. Determine the site templates from step 3 that are completely within the parcels

Note that this algorithm creates many many temporary objects in step 3.

Some thoughts on optimalization:

• You probably can reduce the number of grid points, as some grid points are too close to the edge of the parcels for a possible fit of the site templates. So it may be possible to inwardly buffer the parcels before creating the point grid. This is certainly the case with your site templates, as they are squares.
• The accuracy of this algorithm depends on the distance between the points in the point grid and the step size of rotating the site templates. Smaller values increase the possibility of finding fits, but also create many more temporary objects.
• Your example site templates are squares, so you can suffice with fewer copies in step 3 (after applying a rotation of 90 degrees around the center point you get the original site template).

This may be possible in FME, following an algorithm like this:

1. Create a point grid inside the parcels
2. Move a copy of each site template to every grid point (put the center of the site template on the grid point)
3. Create copies of these copies, and rotate each copy with a different rotation angle around its center point
4. Determine the site templates from step 3 that are completely within the parcels

Note that this algorithm creates many many temporary objects in step 3.

Some thoughts on optimalization:

• You probably can reduce the number of grid points, as some grid points are too close to the edge of the parcels for a possible fit of the site templates. So it may be possible to inwardly buffer the parcels before creating the point grid. This is certainly the case with your site templates, as they are squares.
• The accuracy of this algorithm depends on the distance between the points in the point grid and the step size of rotating the site templates. Smaller values increase the possibility of finding fits, but also create many more temporary objects.
• Your example site templates are squares, so you can suffice with fewer copies in step 3 (after applying a rotation of 90 degrees around the center point you get the original site template).