When I first looked at this, my initial thought was that if the squares on the screen space were solid objects sitting on the texture, and the camera was a bright light, would the mapping on the texture space be like shadows?
stephanie-fu
I'm not sure if this intuition is accurate, but I imagine taking the screen space (chocolate wrapper applied on the screen), drawing squares on it, and "stretching" it back out to restore the grids to perfect squares (smoothing out the chocolate wrapper). The squares will "stretch" as well into all kinds of shapes, depending on how far away the square was from me when I drew it.
danielhsu021202
We can also think of the perspective in terms of magnification and minifiation; Things get smaller as they move away from us, so due to perspective, the area that's meant to be "far away" from us would be considered minified, which is represented as the screen space sampling a large portion of the texture space. Vice versa for magnification and the part of the image that's supposed to be "close to us".
spegeerino
I know this is a very hacky way of doing things in general, but if we're only interested in creating these kinds of mathematical, purely geometric textures, is it possible to create a custom function that can be computed at runtime which gives you the "correct" color values in order to faithfully recapture the texture without causing aliasing?
sylviacx
Thinking about it in the opposite direction of stephanie's comment, imagine drawing those warped rectangles on the 2D texture. Then, imagine wrapping that texture around the floor and viewing the floor from the perspective of a person standing on it. That is what the screen space image captures. Because of the perspective, those warped rectangles will look like perfect squares from the viewpoint of a person standing on the floor.
When I first looked at this, my initial thought was that if the squares on the screen space were solid objects sitting on the texture, and the camera was a bright light, would the mapping on the texture space be like shadows?
I'm not sure if this intuition is accurate, but I imagine taking the screen space (chocolate wrapper applied on the screen), drawing squares on it, and "stretching" it back out to restore the grids to perfect squares (smoothing out the chocolate wrapper). The squares will "stretch" as well into all kinds of shapes, depending on how far away the square was from me when I drew it.
We can also think of the perspective in terms of magnification and minifiation; Things get smaller as they move away from us, so due to perspective, the area that's meant to be "far away" from us would be considered minified, which is represented as the screen space sampling a large portion of the texture space. Vice versa for magnification and the part of the image that's supposed to be "close to us".
I know this is a very hacky way of doing things in general, but if we're only interested in creating these kinds of mathematical, purely geometric textures, is it possible to create a custom function that can be computed at runtime which gives you the "correct" color values in order to faithfully recapture the texture without causing aliasing?
Thinking about it in the opposite direction of stephanie's comment, imagine drawing those warped rectangles on the 2D texture. Then, imagine wrapping that texture around the floor and viewing the floor from the perspective of a person standing on it. That is what the screen space image captures. Because of the perspective, those warped rectangles will look like perfect squares from the viewpoint of a person standing on the floor.