Problem with the size of the Cone of Vision in relation to the Station Point and the Picture Plane

Question

I'm asking this because I don't understand something while studying perspective.

I am curious about whether, in perspective, the distance of SP (station point) should not be set to the actual distance.

For example, I'm sitting on a chair in front of a desk and am trying to draw the desk in front using one-point perspective.
At this time, the distance between me and the desk is very close. Let's assume it's 20cm.
Then, the distance between myself and the picture plane (PP) between me and the desk will be closer.

In comparison, if the height from my eyes to the soles of my feet touching the ground is about 100 cm or more (i.e. eye level), it will be an absurd structure like the picture I attached.

The distance between SP and PP is so close that the cone of vision will be too narrow, and as a result, the field of vision will only be on the horizon line and cannot include objects below it.

Ultimately, if you want to see the objects below, you will need to widen the cone of vision by making the SP distance farther than it actually is.

So in the end, what is the meaning of everything I learned about the relationship between PP and SP? I feel that it is very unnatural to say that the position of SP is the position of view, i.e. 'the position of I'. This is because the actual position or distance I see does not matter, and ultimately the position of SP will have to be set according to the cone of vision.

So, if I want to draw the space that my eyes can actually see, do I forget about my actual location or where the PP is, and only check how wide the cone of vision needs to be and adjust the SP distance accordingly?

Or is there a reason to consider something else I don't understand?

Answer 1

It seems that you are reversing what drives the size of the cone of vision. That cone is determined by your station point (SP), ie where your eye is and the field of view (FOV) you have chosen for your drawing. The cone of vision is completely arbitrary since the field of view can be anything from very narrow (like in your diagram) or very wide.

The picture plane (PP) is a virtual construct. It is set to contain the FOV while being perpendicular to the line from the station point to the scene you are drawing. That is the line that forms the center of your cone of vision. The PP can exist anywhere on that line and as long as it remains centered and perpendicular to it, the scene it captures will be the same. For convenience we imagine the picture plane as coinciding with the drawing surface but it does not have to be at the same point in space. You could imagine it behind the objects you are drawing, as long as you are projecting from the same SP the objects you are capturing will land at the same points on the drawing.

What it sounds like, when you want to change the SP in order to capture more of the space you are drawing, what you are trying to do is fit more into the cone of vision. Yes, moving the station point back will do that if you keep the same angle for your FOV because now that cone is wider where your subject matter is (the subject is further down the cone to a wider part of it). So would expanding your FOV. That makes the cone of vision wider, bringing the subject matter into frame, but it does so without changing your SP. Think of it as making the PP wider if you are holding its location at the same point relative to the SP.

tl;dr: The cone of vision is determined only by the station point which anchors its tip, the direction of view which sets its direction, and the FOV which determines its width.

Answer 2

To me it sounds like your confusion comes from the size of the cone of vision. Yes, it is tiny in your diagram, and no, this is not how we as humans experience the world. Mostly because our eyes are constantly in motion, shifting the cone of vision around until the image our brain perceives is much larger.

Try this experiment:

Take the cardboard tube from an empty roll of toilet paper or a similar tube. Hold the tube in front of your eye and look at the table without moving the tube. What you see is a very narrow cone of vision like you drew in your question. This is objectively all you can see at one moment in time.

If you want to see your feet, you have to move the cardboard tube down. In that position you won't be able to see the horizon line at all.

It feels unnatural to us because we move our eyes around all the time. Subjectively we humans perceive a wider cone of vision because of our eye movement.

For a drawing this means that it looks more natural to us if the cone of vision is wider than in your diagram