Writing this comment while at 26:27 in the lecture recording--where professor says we can discuss the mathematical details of this in the comments...I am looking at this link to think about the math behind this (not very well, I may add): https://nicolbolas.github.io/oldtut/Positioning/Tut04%20Perspective%20Projection.html
For 2D to 1D, we are creating a kind of orthographic projection from the 2D space to be represented as colors on a line. So is this picture a 1D to 1D case where we can just use geometry of trapezoids and our knowledge of the 2 lines/planes in a coordinate plane to map onto the plane demonstrating perspective? Or is this just showing the side of 2 2D figures? If neither of these are the case, what is the math behind it?
Tap me if this doesn't make sense, and I'll try to explain my question better
grafour
I'm still a little confused. the prof says that we need to divide everything by z2. What is z2 and how does the division work? Is this something we should know or is this just a note to keep.
stephanie-fu
If this figure was drawn with orthographic projection, would the dashed lines be horizontal, spanning more of the image plane?. How would that image then be captured by our eye (the dashed lines between our eye and the image plane must still be diagonal and converge on our pupil right)?
spegeerino
@grafour (Someone please correct me if I'm wrong, I don't know exactly how perspective interpolation works) I think he meant "z too," as in we have to divide each length in the texture to something corresponding to its distance from the camera (the z-coordinate in camera space), as the lengths shrink from our perspective as they get further away from the camera. In order to combat this GPUs have their own way of interpolating the texture coordinates after projecting to the image plane which maintains the perspective you would expect, which is more complicated than just dividing by z in the general case I think (Edit: I don't think it actually is more complicated than this, it's just some geometry that needs to be done, but as the professor said in class divisions used to be quite expensive so people wanted to avoid them as much as possible).
Writing this comment while at 26:27 in the lecture recording--where professor says we can discuss the mathematical details of this in the comments...I am looking at this link to think about the math behind this (not very well, I may add): https://nicolbolas.github.io/oldtut/Positioning/Tut04%20Perspective%20Projection.html
For 2D to 1D, we are creating a kind of orthographic projection from the 2D space to be represented as colors on a line. So is this picture a 1D to 1D case where we can just use geometry of trapezoids and our knowledge of the 2 lines/planes in a coordinate plane to map onto the plane demonstrating perspective? Or is this just showing the side of 2 2D figures? If neither of these are the case, what is the math behind it?
Tap me if this doesn't make sense, and I'll try to explain my question better
I'm still a little confused. the prof says that we need to divide everything by z2. What is z2 and how does the division work? Is this something we should know or is this just a note to keep.
If this figure was drawn with orthographic projection, would the dashed lines be horizontal, spanning more of the image plane?. How would that image then be captured by our eye (the dashed lines between our eye and the image plane must still be diagonal and converge on our pupil right)?
@grafour (Someone please correct me if I'm wrong, I don't know exactly how perspective interpolation works) I think he meant "z too," as in we have to divide each length in the texture to something corresponding to its distance from the camera (the z-coordinate in camera space), as the lengths shrink from our perspective as they get further away from the camera. In order to combat this GPUs have their own way of interpolating the texture coordinates after projecting to the image plane which maintains the perspective you would expect, which is more complicated than just dividing by z in the general case I think (Edit: I don't think it actually is more complicated than this, it's just some geometry that needs to be done, but as the professor said in class divisions used to be quite expensive so people wanted to avoid them as much as possible).