Source image
Source image is a disk shaped anamorphic one shot 180° image which was presumably computer generated as a projection of a virtual 3d environment on a perfect semi sphere. After making sure it is centeredand the file is perfectly square..
Filter
Photoshop -> Filters -> Distorsion -> Polar Coordinates - polar to rectangular filter is applied.
Compression
The image was compressed to fit only the northern hemisphere
Gores
Flaming Pears Flexify 2
Filter applied with Mercator as a source
and 12 gores as a target. The ratio ofthis image should be stretched
to be 1:2 because it is horizontally the perimeter and vertically
half the perimeter.
I actually should have selected equirectangular as a source projection,
because the source is not a Mercator projection
Flower
The 12 resulting gores in a Flower Petal pattern (each segment is turned 30°)
Conclusion
The Flexify 2 filter introduces a hole in the middle and wraps the image around that. This isn't the desired function. Flexify 2 offers to add an overlap for the glue but only solid colors are available to choose, better (less visible) would be if the pattern would continue. Flexify offers other input projections like mirror ball or one shot which one would think could allow direct image procession without the polar to rectangular conversion, but those settings give inexpected results. Stitching the gores to the Flower Petal is time consuming and always slightly inaccurate, thus not the optimal workflow.