Based on this diagram, it looks like the edges of the cube aligned with the z-axis, which are parallel in reality, would all in the perspective projection intersect with the origin if they were to be extended.

Is this a property of the pinhole camera projection in general? That is, if an edge from point (x, y, z1) to (x, y, z2) is visible in the perspective projection, will it necessarily intersect with the origin if extended?

superbluecat

What kind of transformation should we make if the direction of the camera is not parallel to an axis? Should we spin the coordinates by making a matrix multiply?

Actually I think that the projection formula when camera is parallel to z is a very special case of a more general formula. What exactly is it?

saphirasnow

I see this cube very differently depending on whether I assume the smaller square is in front or in back. How would we encourage the viewer toward one interpretation or the other?

vtnguyen

I think this cube somehow doesn't really look like a cube. At first glance it appears more like a cuboid or even a cross-section of a square pyramid. Is this because the pinhole is too close to the cube, and how do we ensure correct representation to the viewers?

anag

Is the reason for the distortion of the front and back sides of the cube due to the unit focal length of the camera (distance from c to the image plane)?

rbm

I believe the distorted view would be because this is an orthographic view.

dab

Let's say we assume that right is positive z, up is positive y, and going from the canvas towards us is positive z. In that case, I would have assumed that the smaller square made up by the points with negative z (E, F, G, H) would have been on the top right of the bigger square since that is the perspective I would have imaged for a camera at (2, 3, 5) looking at a cube at (0, 0, 0), which would be been looking down and to the left. Is there an explanation for this disconnect?

Midoriya

Is there a reasonable explanation for the fact that some edges that are supposed to be parallel do not look parallel? I literally tried with my camera and I couldn't find an angle to reproduce this picture.

derk

Why do some of the cube edges appear skewed and not parallel despite the cube's axis-aligned model definition? Is this result just the nature of perspective projection? Will the degree of edge "skewedness" vary with camera intrinsics, distance, and the real size of the object we are viewing?

Murrowow

I believe the lines are supposed to be parallel so its very interesting that it doesn't appear to be that way. It would be nice to have an explanation as to why that is the case and maybe converse a little on how exactly different angles would distort an image.

kinematics

You mention that the procedure is deterministic. Is there a reason for this to be considered important or good?

ScreenTime

Why does the back side look bigger than the front side?

Based on this diagram, it looks like the edges of the cube aligned with the z-axis, which are parallel in reality, would all in the perspective projection intersect with the origin if they were to be extended.

Is this a property of the pinhole camera projection in general? That is, if an edge from point (x, y, z1) to (x, y, z2) is visible in the perspective projection, will it necessarily intersect with the origin if extended?

What kind of transformation should we make if the direction of the camera is not parallel to an axis? Should we spin the coordinates by making a matrix multiply?

Actually I think that the projection formula when camera is parallel to z is a very special case of a more general formula. What exactly is it?

I see this cube very differently depending on whether I assume the smaller square is in front or in back. How would we encourage the viewer toward one interpretation or the other?

I think this cube somehow doesn't really look like a cube. At first glance it appears more like a cuboid or even a cross-section of a square pyramid. Is this because the pinhole is too close to the cube, and how do we ensure correct representation to the viewers?

Is the reason for the distortion of the front and back sides of the cube due to the unit focal length of the camera (distance from c to the image plane)?

I believe the distorted view would be because this is an orthographic view.

Let's say we assume that right is positive z, up is positive y, and going from the canvas towards us is positive z. In that case, I would have assumed that the smaller square made up by the points with negative z (E, F, G, H) would have been on the top right of the bigger square since that is the perspective I would have imaged for a camera at (2, 3, 5) looking at a cube at (0, 0, 0), which would be been looking down and to the left. Is there an explanation for this disconnect?

Is there a reasonable explanation for the fact that some edges that are supposed to be parallel do not look parallel? I literally tried with my camera and I couldn't find an angle to reproduce this picture.

Why do some of the cube edges appear skewed and not parallel despite the cube's axis-aligned model definition? Is this result just the nature of perspective projection? Will the degree of edge "skewedness" vary with camera intrinsics, distance, and the real size of the object we are viewing?

I believe the lines are supposed to be parallel so its very interesting that it doesn't appear to be that way. It would be nice to have an explanation as to why that is the case and maybe converse a little on how exactly different angles would distort an image.

You mention that the procedure is deterministic. Is there a reason for this to be considered important or good?

Why does the back side look bigger than the front side?