Fisheye: Best of Both Worlds

The lens I used for my photo yesterday was extreme: a 7.5 mm ultra wide angle lens. Yet I straightened it out, mostly. Above, one sees a 7.5 mm fisheye shot of a mall (on the left) and a converted equirectilinear shot (on the right). An equirectilinear projection straightens out the vertical lines especially. Now one has the best of both worlds: fisheye and equirectilinear. I couldn't find instructions on the Internet -- I achieved the above like this. Call up the Hugin panorama photo stitcher. Load the original fisheye image. Select Interface > Expert. Select Photos. Click on the filename. Lens type: Circular fisheye. Focal length: 10 (in my case, not 7.5 as expected). Some experimentation will obtain the right focal length. Focal length multiplier: 1.524 (default). Select Stitcher. Horizontal field: up to 179. Vertical field: up to 179. This sets the photo borders. Click on Interface > Simple. Projection > Equirectangular Panini (or try another projection). Use Crop to snip off black space. Click on Assistant to complete the process. Stretch the photo to match its original borders OBSERVATION: As seen above, one's losses are not bad. One loses nothing at the centre top and bottom, and nothing at the centre right and left. One loses the corners.