Interesting seeing how elementary geometric ideas, such as similar triangles and parallel lines, are heavily used in ray tracing. One thing I was curious about is what happens when we don't have parallel lines? For instance, the whole reason we can get the ratios on the bottom of this slide is due to ray h_o, line segment h_0h_i, and ray h_i all being parallel with each other. When these lines are NOT parallel, is there still a way to get certain ratios? I'm guessing we may have to break down the lines into it's sine and cosine segments?
spegeerino
@ShonenMind I'm not sure how much we can do with non-parallel lines using the same argument, as the lens will bend light to a point other than the focus in this case. However, if you have two rays that bend to two intersections points of equal distance (even if it's not the focal length) it may be possible to compute these kinds of ratios using the same approach, although it might be harder to compute when this would occur.
Interesting seeing how elementary geometric ideas, such as similar triangles and parallel lines, are heavily used in ray tracing. One thing I was curious about is what happens when we don't have parallel lines? For instance, the whole reason we can get the ratios on the bottom of this slide is due to ray h_o, line segment h_0h_i, and ray h_i all being parallel with each other. When these lines are NOT parallel, is there still a way to get certain ratios? I'm guessing we may have to break down the lines into it's sine and cosine segments?
@ShonenMind I'm not sure how much we can do with non-parallel lines using the same argument, as the lens will bend light to a point other than the focus in this case. However, if you have two rays that bend to two intersections points of equal distance (even if it's not the focal length) it may be possible to compute these kinds of ratios using the same approach, although it might be harder to compute when this would occur.