Photoshop :: Pixel-slop In Photoshop Image Rotation

See three small bitmaps attached: <<original.bmp>>; <<45cw.bmp>>; <<45ccw.bmp>>.The original is a simple 21x21 pixel test pattern, black except for white pixels in the center and corners.  It's appearance should be the same whether rotated 45 deg clockwise or counterclockwise, and the appearance should keep the symmetry of the original.I used "Bilinear Interpolation".

I used a gamma = 1 profile, and to be extra-safe set Edit>Assign Profile>Don't Color Manage ...I set the background color to black in the toolbox.  Thank you John Joslin.Then I rotated the original image 45 deg clockwise and counterclockwise to make the other two files.  Why to the resulting images look so different?  Why are they lacking in symmetry?  With the other interpolation methods too, clockwise and counterclockwise rotations give quite unlike images.  A partial explanation could be that Photoshop rotates about a point not in the image center, but this doesn't explain enough.

I tried 20x20 patterns which showed similar problems. I'm mostly interested in bilinear interpolation because this is supposed to conserve the total pixel value.  Each white pixel in the original has value 255, so the blob resulting from this pixel should have total value 255.  Look at <<45cw.bmp>>.The blob on the left has total value 69+94+13+5+18+1=200.  The blob on the right is an almost perfect antipode with total value 1+18+6+13+95+68=201. 

The blob at the bottom doesn't resemble the side blobs and has total value 42+56+40+3+55=196.  The blob at the top has total value 40+41+56=137.  Clearly Photoshop has lost the top of the top blob.  (It also does this with 45 deg counterclockwise rotation, and also with 135 deg rotation.)  The blob in the center has total value 49+49+48+47=193. 

All of the blobs fall far short of 255.  Photoshop might be excused for messing up edge pixels, but not a central pixel. Photoshop messes up rotation at the single pixel level.  I made a test pattern with clusters of 4 white pixels and the rotation of this did conserve the total value for the central four.  Edge pixels still showed problems.  Photoshop image rotation appears to be based on sloppy code.