Why the puzzle always has exactly one answer
A daily puzzle has to be solvable every day, with no exceptions and no one checking by hand. In Anamorph that is not achieved by testing the output. It is achieved by building the puzzle in a way that cannot produce a bad one.
The rule
Start with the finished picture, flat, in one piece. Choose a viewpoint. Then take any piece of that picture and do exactly one thing to it:
Move it directly away from the viewpoint, along the straight line joining them, and make it bigger by the same factor. Move it twice as far, make it twice as big. Move it a tenth further, make it a tenth bigger.
That piece now sits somewhere else entirely in space, at a different size, but from that one viewpoint it covers exactly the same part of your field of view as before. It has to. It got further away and larger in the same proportion, and those two effects cancel precisely.
This is the same reason you can blot out the moon with your thumb. The moon is vastly bigger and vastly further away, and at your eye those two facts cancel to the same angular size. The thumb and the moon are, from that one point, interchangeable.
Why this guarantees a solution
Apply the rule to every piece, each with its own random distance, and you get a cloud of fragments scattered through space at wildly different depths and sizes. From the chosen viewpoint, every piece still lands exactly where it did in the original picture, because every piece was moved along its own sightline and rescaled to compensate.
So the answer is not something the generator searches for and hopes to find. The answer is the input. The puzzle is constructed backwards from the viewpoint it will be solved from, which means an unsolvable arrangement is not a rare bug. It is not expressible.
The projection is exact rather than approximate, and we check that: the error between where a fragment lands and where it should land is about three parts in ten thousand billion, which is the precision limit of the arithmetic and not a property of the design.
Why it looks like nothing from anywhere else
Move even slightly off the viewpoint and the cancellation stops working. Each fragment now shifts by an amount proportional to how far along its sightline it was pushed, and every fragment was pushed a different distance. Near ones barely move, far ones swing across the view. The picture does not blur, it disassembles, and it does so quickly.
That is why a near miss is not a slightly worse picture. It is a different picture, or no picture at all.
The part that is genuinely hard
The rule above gets you a solvable puzzle in an afternoon. It also gets you an easy one, because the construction leaves fingerprints that point straight back at the answer.
If every fragment lies flat and parallel to the original picture, you can rotate until the pieces look square on, and you are there. So each fragment sits on its own randomly tilted plane instead, with its corners traced onto that plane. A flat four cornered shape textured from its corners still projects perfectly, so the guarantee survives, and the flatness tell is gone.
If the fragments are free to sit at any depth, the cloud fills the cone of vision from the answer, and a cone tapers. The cloud's own silhouette becomes an arrow. So the fragments are confined inside a ball instead, and a ball looks the same from every direction.
If only the picture's own pieces are present, they still cluster in the region the picture occupies, and their sizes still grow with distance in a way that points home. So the ball is packed with decoy fragments that carry no part of the picture, drawn from the same size range but with sizes deliberately unrelated to their depth, in the same material, brightening in exactly the same way.
The governing principle
All of those fixes are the same fix, stated once:
Anything whose appearance depends on the answer alone is a leak. If a property is shared across many objects, it has to be randomised per object, or it becomes a readout.
That is why the proximity glow warms every fragment equally, decoys included. A glow that lit only the real pieces would tell you which ones matter, and knowing which pieces carry the picture is most of the way to knowing where to stand.
The honest version of the whole thing: the geometry contains its own answer, because it has to. What makes it a puzzle is that reading the answer out of it takes more work than simply looking for it. You can try today's if you want to test that.