First, take a look at these answers:
At what point does 1 point perspective become 2 point perspective?
Finding the possible vanishing points in a landscape
Now. Let me play with the answer.
You can not have a 90° angle from a perspective. If it is at 90° It would be an orthographic view.
We can only have the "illusion" of 90° angles from a perspective.
A perspective is a projection, and any projection has a deformation. It flattens, it compresses, it changes angles.
One thing that you need to explore is the field of view.
"The Cone of vision" is a specific type of field of view, that mimics somehow a normal field of view. Normal is a relative term. People with some condition on the sight can have different fields of view, people that only see with one eye or glaucoma for example.
In photography, a "Normal" lens for a normal field of view is let's say a 40-50 mm lens.
But we can have more field of view using a wide lens. What this does is squeezing more information about the surroundings that we normally have in an area, the visor. This example starts to look distorted.
The most extreme of these views is a 360° panorama where we can see everything around us on an image in front of us. Remember this is a projection.
If we project this again, imagine a big spherical screen around us, the image will look normal again because the information of the objects behind us are again behind us.
Let me manipulate a bit the second image. Here is a crop.
Now we do not perceive it as distorted as before:
- If you move outside the "field of view", (to some degree) but you do not change the angle of the field of view, you are simply doing a camera movement, like a "panning" rotating the camera. The vanishing points will move relative to the new field of view. But everything will keep the "proportions".
- If you want to see these things outside the field of view but without moving the "camera" you need to widen this, so things will start to "distort". What happens is the vanishing points will start to get close each to another. At one moment instead of having 2 vanishing points at the horizon, you could have 3 and even 4!
But this initial distortion could be simply of "scale".
- But if you try to compensate this wider field of view with the framing of the object you are changing completely the point of view. Now it is a different drawing.
- One last thing to consider. the main factor in "distortion" is the proportions.
You can only force a vanishing point to some extent without forcing it to lose proportion to another vanishing point.
A 2 point perspective is, in reality, a 3 point perspective without considering the 3rd.
If you force two points on the horizon but you do not compensate and making the third one effective you can simply deform your image.
A couple more ideas.
Every object has several vanishing points. In fact, there is an infinite number on each object and it is independent of another's object.
The fact that we use a 2 point perspective is because we are used to building things in orthogonal angles. Walls, ceilings, streets. We assume that a box is a cube, but it could not be the case. So be open to playing with more vanishing points than you expect.
Images by pixabay.com