# Is it possible to paint an oblique (perspective) anamorphic illusion on a three dimensional surface viewable from all angles as you pass it?

So hypothetical situation: Let's say I have a hallway, say 10 feet wide. On one side of this hallway, I erect a three-dimensional facade from floor to ceiling, so that it sticks out from the wall. I feel like the likeliest to work may be a semicylinder (cylinder cut lengthwise), but I'm not really sure. To provide a visual example (you'll just have to imagine that these are the correct dimensions and shapes):

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What I want to know is, would it be possible to paint such a facade in a way that, if a person of the proper height were to walk from one end of the hallway to the other, it would create the illusion at all points along their walk that they were passing a flat expanse of wall? So as the viewer enters the hallway and walks along it, it appears at all angles along that path to be a normal hallway with no protrusion. Assume that the painting is photorealistic for this hypothetical.

If this isn't possible with a semicylinder, is there a configuration of faces that would make this possible? Or is it simply impossible to create a perspective illusion viewable from that many angles, even controlling for the height and position of the transect the viewer walks?

(Apologies for poor question tags, apparently I'm not allowed to create proper tags for my question as a new user.)

• Do you mean that through painting it in a certain way the protrusion would appear from every angle, or as many as possible, to not be there?
– Joachim
Apr 29 at 18:13
• Is the idea to have what looks like a normal, uniformly painted, wall on the side of the hallway, and from any point in the hallway it looks like there is no semicylinder sticking into the hallway (so what you see on the protrusion from the ends of the hallway looks like what's beyond the end of the hallway on the other side), or the wall and semicylinder will have a painting of some object, and at any point in the hallway the painting will look like it is on a flat wall? Apr 29 at 18:35
• Yes, the intention of the illusion would be to make it appear as if it were, in fact, just a normal hallway with no protrusion. So the painting would need to include the floor and ceiling in some form of perspective as well. Now that I think about it some more, for it to work at all, it would have to not stick out far enough to require the ends of the hall to be included in the painting, as that would not work when viewing straight on. I've edited the original post to clarify. Apr 30 at 3:01

You could make it work from a single vantage point, but not from numerous or continuously changing vantage points.

Whatever shape sticks out from the wall (semicylinder or other), I'll call that the protrusion. Imagine that it was transparent so you could see through it to the features you need to reproduce, such as the line where the wall meets the floor, or the back corner where the side wall meets the back wall. From a particular vantage point, you could look through the protrusion to a feature you need to reproduce and direct someone to mark where your sight line intersects the protrusion surface. If you do that for all of the features, you could use those marks to paint the view. It will have the right perspective to look like what you see from that position.

When you do that from the hall entrance, the closest half of the protrusion will be visible. Features, like where the wall meets the floor, at the outer visible edge of the protrusion will be aligned with your sight line to the actual feature immediately adjacent to the edge, so the line would look continuous. If you repeat the process from the other end of the hall, the other half of the protrusion will be visible.

As you walk from the end of the hall toward the protrusion, the end of the drawn line will no longer match the visual location of the feature, so the line won't look continuous. From the middle of the protrusion, you can see the entire thing. From that vantage point, your sight lines to the features are different, as well as where those lines intersect the protrusion surface. So reproducing that vantage point will yield a different image.

Also, if the protrusion is curved, what looked like straight lines from the original vantage point will look like curved lines from another vantage point.

To further complicate things, all surfaces would need to be uniform colors (e.g., a wood floor would have wood grain detail). In real life, objects farther away look smaller. From the hall entrance, when you look through the protrusion to the farthest features to reproduce, any detail or texture would need to be painted smaller on the protrusion surface. When you walk toward the protrusion, the relative size of those details will become wrong.

Another complication -- even if you could perfectly reproduce the features and perfectly light it so no shadows gave it away (such as where the object meets the wall), your eyes would tell you it isn't a flat wall. Eyes accommodate for distance (the closer the object, the more your eyes turn toward the center). It's automatic so that what you're looking at is centered where your eyes discriminate the most detail, and your brain uses it as a clue to the object's distance. Within a normal hallway, the distance to the object as you walk past it would probably be within the range that your brain would detect a discrepancy if you were looking at it.

Having said all that, if you could make the protrusion really long, so you can't easily see the far end from one side, and if there were no vertical features like a back corner, the only visible reference would be an adjacent portion of the protrusion. You could map the sight line intersections at small intervals from one end of the hall to the other, and create a "moving average" of the line. With no other visual reference, it might be hard to notice that the wall isn't flat.

• Thanks, this explanation makes it really easy to visualize the issues. Apr 30 at 15:00