Very cool to see the output of this graphics algorithm! Wondering if there is a simple algorithm to determine which edges to draw so that edges hidden by faces of the cube would not be visible.
bcagan
Its definitely interesting to see that because the camera's angle wasn't changed, but its position was, the two faces parallel to the "lens" remained squares, but the other faces were warped.
peanut
Nice demonstration. A small piece of advice - Actually it took me a while to understand why a standard cube looks this way through that camera. I think it will be more explicit to understand if we can have a vivid picture showing the mapping between 3d cube and this projected cube!
dnialh
One thing I found weird about this projection is that this cubed seems significantly warped by the projection (the back face is about half the size as the back half). Playing around with a cube in real life, this effect seems more magnified than any effect I can get by moving around the cube in front of my eyes. Is there something weird about the specific projection we use, or another explanation might be that in real life, my brain has already auto-corrected what I see, and even though I should be seeing the back faces of the cube as much smaller, my brain already understands that it the same (or about the same) size as the front face.
bcagan
I quickly tried out placing a cube in paint 3D and trying a similar camera movement (or movement of the cube, in this case) and it seemed somewhat odd still but less so, which makes me think that either when the one sees both the back and front of the cube, one doesn't fully interpret it as a cube, or, the lack of any shading on any of the faces makes one interpret it as a bunch of lines making up a cube, as supposed to a cube object. Thats all me guessing though, of course, I assume we will get a better explanation of this later in the course. Or using Paint 3D isn't the same as what we did in class in which case this doesn't mean anything....
ecdeo
Basically my entire 112 final project is covered by a single lecture. Nice!
FeiFeiFei
Nice to see the very first algorithmic way to produce a visual representation of a cube! As other comments have mentioned too, the projection is not so perfect, as the front of cube looks disproportional to the back of the cube. Maybe a more complicated algorithm we will come across later in the course will solve the issue. For now, I am just guessing if the reason behind the disproportion is due to the imperfection of our "pinhole" model used to create projection. According to my knowledge about physics, our eyes are actually rendering scenes based on convex lens which might be similar to "pinhole" but a little bit different. I am wondering if that is the reason resulting in the imperfection.
peanut
Nice discussions here! I went over your comments and rethink about this, we admit there is difference between human eyes and pinholes, I am not sure what it is exactly, but human eyes have some correction mechanism, which makes me feel the pinhole projection less truthful. But this is out of calculations, so I had to accept the truthiness here.
0x484884
I was also thinking about why the cube looks kind of weird here and came up with a couple ideas although I'm not sure if any of them are correct:
- We are looking perpendicular to the face of the cube, but the cube isn't at the center of our vision so its like we're staring at the origin and then looking at the cube in our peripheral vision. Normally, we would look right at the cube and since it is not centered at the origin, we would see it at an angle that is not perpendicular to the face. It seems like using just the z distance to scale doesn't work perfectly in this case because the distances do not just rely on the z direction.
- I don't think our retinas are flat like the film in the pinhole camera so we are actually projecting the image onto a curved surface which would distort parts of the cube that are further away, even if the z coordinate is the same (so the top right corner of a face would look smaller than the bottom left.
- We are much closer to the cube than we would be in most normal situations so its just a weird view. I think being really close also would magnify the effects of the things I mentioned earlier.
eryn
Got the exact same result as in the slide! Yay
Jamie
It's pretty cool for me to practice and draw the calculated results out by hand in a class. I like the way of the class is presenting! :D
Very cool to see the output of this graphics algorithm! Wondering if there is a simple algorithm to determine which edges to draw so that edges hidden by faces of the cube would not be visible.
Its definitely interesting to see that because the camera's angle wasn't changed, but its position was, the two faces parallel to the "lens" remained squares, but the other faces were warped.
Nice demonstration. A small piece of advice - Actually it took me a while to understand why a standard cube looks this way through that camera. I think it will be more explicit to understand if we can have a vivid picture showing the mapping between 3d cube and this projected cube!
One thing I found weird about this projection is that this cubed seems significantly warped by the projection (the back face is about half the size as the back half). Playing around with a cube in real life, this effect seems more magnified than any effect I can get by moving around the cube in front of my eyes. Is there something weird about the specific projection we use, or another explanation might be that in real life, my brain has already auto-corrected what I see, and even though I should be seeing the back faces of the cube as much smaller, my brain already understands that it the same (or about the same) size as the front face.
I quickly tried out placing a cube in paint 3D and trying a similar camera movement (or movement of the cube, in this case) and it seemed somewhat odd still but less so, which makes me think that either when the one sees both the back and front of the cube, one doesn't fully interpret it as a cube, or, the lack of any shading on any of the faces makes one interpret it as a bunch of lines making up a cube, as supposed to a cube object. Thats all me guessing though, of course, I assume we will get a better explanation of this later in the course. Or using Paint 3D isn't the same as what we did in class in which case this doesn't mean anything....
Basically my entire 112 final project is covered by a single lecture. Nice!
Nice to see the very first algorithmic way to produce a visual representation of a cube! As other comments have mentioned too, the projection is not so perfect, as the front of cube looks disproportional to the back of the cube. Maybe a more complicated algorithm we will come across later in the course will solve the issue. For now, I am just guessing if the reason behind the disproportion is due to the imperfection of our "pinhole" model used to create projection. According to my knowledge about physics, our eyes are actually rendering scenes based on convex lens which might be similar to "pinhole" but a little bit different. I am wondering if that is the reason resulting in the imperfection.
Nice discussions here! I went over your comments and rethink about this, we admit there is difference between human eyes and pinholes, I am not sure what it is exactly, but human eyes have some correction mechanism, which makes me feel the pinhole projection less truthful. But this is out of calculations, so I had to accept the truthiness here.
I was also thinking about why the cube looks kind of weird here and came up with a couple ideas although I'm not sure if any of them are correct: - We are looking perpendicular to the face of the cube, but the cube isn't at the center of our vision so its like we're staring at the origin and then looking at the cube in our peripheral vision. Normally, we would look right at the cube and since it is not centered at the origin, we would see it at an angle that is not perpendicular to the face. It seems like using just the z distance to scale doesn't work perfectly in this case because the distances do not just rely on the z direction. - I don't think our retinas are flat like the film in the pinhole camera so we are actually projecting the image onto a curved surface which would distort parts of the cube that are further away, even if the z coordinate is the same (so the top right corner of a face would look smaller than the bottom left. - We are much closer to the cube than we would be in most normal situations so its just a weird view. I think being really close also would magnify the effects of the things I mentioned earlier.
Got the exact same result as in the slide! Yay
It's pretty cool for me to practice and draw the calculated results out by hand in a class. I like the way of the class is presenting! :D