A short history of perspective
Linear perspective feels like the natural way to draw, which is exactly why it is worth remembering that for most of human history nobody drew that way. It is a technique, it has an inventor and a date, and anamorphosis is what happens when you turn it around.
Before
Egyptian painting shows each thing from its clearest angle: a face in profile with a front facing eye, shoulders square on. Medieval European painting sizes figures by importance, so a saint towers over a merchant standing next to him. Neither is incompetent. Both are answering a different question, which is what is this a picture of, rather than what would this look like from here.
Roman wall painting at Pompeii gets closer, with receding architecture and convergent lines, but the lines do not converge on a single point and the space does not hold together. They had the intuition without the rule.
Florence, and a hole in a board
The rule arrives with Filippo Brunelleschi, in Florence, some time around 1413 to 1425. Brunelleschi was an architect, and the demonstration he devised is more like an experiment than a painting.
He painted the Florence Baptistery on a small panel, in correct perspective, from a precise spot just inside the door of the cathedral opposite. Then he drilled a hole through the panel at the vanishing point. You stood on the spot, held the painted side away from you, looked through the hole at the actual Baptistery, and raised a mirror in your other hand to catch the painting. Lower the mirror and you saw the building. Raise it and you saw the panel. They matched.
The claim being made was not that the painting was beautiful. It was that the painting was correct, testably, from one position. That is a different kind of claim, and it is the beginning of the idea that a picture is a slice of a cone of sightlines.
Writing it down
Brunelleschi left no treatise. Leon Battista Alberti did, in De pictura in 1435, which set out the construction so that any painter could follow it: a horizon at eye height, orthogonals converging to a single vanishing point, a scheme for spacing receding lines correctly. Piero della Francesca, both painter and mathematician, went further in De prospectiva pingendi, working through the hard cases.
Within a generation, perspective had gone from a demonstration to a professional skill, and then to something so ordinary that its absence looks like a mistake.
Turning it around
Here is the part that matters for anamorphosis. Once you have a rule that takes a scene and a viewpoint and tells you what marks to make, you can hold the marks fixed and ask what viewpoint they imply. Or, more interestingly, you can choose an absurd viewpoint on purpose and see what marks come out.
Leonardo did exactly that around 1485 with a stretched eye and child's head in what is now the Codex Atlanticus, the earliest known anamorphosis in Western art. Holbein made it the centre of a major painting in 1533, in The Ambassadors. By 1638 Jean-Francois Niceron had published systematic instructions.
So anamorphosis is not a rebellion against perspective. It is perspective taken completely seriously. If a picture is what arrives at a point, then choosing a strange point is a legitimate thing to do, and the strangeness lives in the marks rather than in the method.
What it is not
Linear perspective is not how vision works, and it is worth being clear about that. You have two eyes, they move constantly, and your visual field is not a flat rectangle. What perspective models is a single fixed eye looking through a window, which is a simplification, and a very productive one. It is also exactly what a camera does, which is why photographs obey the same rules and why perspective still feels like truth.
It is also the reason a picture built for one viewpoint works so well in a photograph and only adequately in person. One lens, one point, no argument. That is discussed in how pavement art works.
Our daily puzzle lives entirely inside this history. It is built with the same construction Alberti wrote down, aimed at a viewpoint we do not disclose, and your job is to find the place the picture was made for.