This section of the lecture confused me a lot, but with a little help from Google Bard (I uploaded a couple slides and asked it to explain) and YouTube, I have a better idea of things.
The Barycentric Interpolation that's a weighted average (as we learned in the previous slides) is an "Affine Transformation." It works great for 2D texture mappings but doesn't work hold for 3D environments because it doesn't take into account depth or the "divide by z" that happens when you do the Pinhole Transformation (see lecture 5).
To fix this, we need to do a "Perspective-correct Interpolation." I don't think Ren explained how to do this (correct me if I'm wrong).
Is there a specific reason for the patterning itself? Why does baycentric interpolation not accounting for depth change the calculation such that there are two "halves" that are tilted?
AbhiAlderman
This topic confused me a lot as well, but @colinsteidtmann your comment and the video you sourced helped me a lot! I did not even think to account for the z axis when it comes to these 2D interpolations, but it makes sense now that I think about it. I think I have a more intuitive understanding of Barycentric interpolations now, so thank you for that.
sueyoungshim
I'm still confused about what creates the diagonal distinction of the second image. Why is it not the upper/lower half or left/right half? And is the barycentric interpolation the same as the affine interpolation?
This section of the lecture confused me a lot, but with a little help from Google Bard (I uploaded a couple slides and asked it to explain) and YouTube, I have a better idea of things.
The Barycentric Interpolation that's a weighted average (as we learned in the previous slides) is an "Affine Transformation." It works great for 2D texture mappings but doesn't work hold for 3D environments because it doesn't take into account depth or the "divide by z" that happens when you do the Pinhole Transformation (see lecture 5).
To fix this, we need to do a "Perspective-correct Interpolation." I don't think Ren explained how to do this (correct me if I'm wrong).
Sources: https://www.youtube.com/watch?v=VdLZCyHNdHc&list=PLqVt3VSe1-ZburMezbglEp3ufrhoYqnt6&index=6
Is there a specific reason for the patterning itself? Why does baycentric interpolation not accounting for depth change the calculation such that there are two "halves" that are tilted?
This topic confused me a lot as well, but @colinsteidtmann your comment and the video you sourced helped me a lot! I did not even think to account for the z axis when it comes to these 2D interpolations, but it makes sense now that I think about it. I think I have a more intuitive understanding of Barycentric interpolations now, so thank you for that.
I'm still confused about what creates the diagonal distinction of the second image. Why is it not the upper/lower half or left/right half? And is the barycentric interpolation the same as the affine interpolation?