So how the 3D points get converted to 2D? I thought it should be prospective projection does the job but now it seems like the prospective projection only transform objects into a normalized cube for clipping?
kshen
at this stage, how do we still have a depth per (x,y) screen coordinate? didn't we divide out the homogenous w depth so that we have a coordinate of form (x/w, y/w, 1) in order to project to 2D to begin with?
isalinas
@Gyro I think transforming objects into a normalized cube goes hand in hand with transforming 3D into 2D. Think of a cube in 3D; with the projection transform, the points near the far plane come closer together, so the vertices which define the back of the cube (closer to the far plane) also become closer together and appear smaller. When these vertices are drawn on the screen, this tranformation gives the illusion that the back of the cube is smaller than the front and therefore farther. I wish I could explain further, but I think the answer to @kshen’s question could help complete my intuition. How do we determine the depth of each vertex? Do we save the depth as a separate variable associated with the coordinate [x/w, y/w,, 1]^T?
So how the 3D points get converted to 2D? I thought it should be prospective projection does the job but now it seems like the prospective projection only transform objects into a normalized cube for clipping?
at this stage, how do we still have a depth per (x,y) screen coordinate? didn't we divide out the homogenous w depth so that we have a coordinate of form (x/w, y/w, 1) in order to project to 2D to begin with?
@Gyro I think transforming objects into a normalized cube goes hand in hand with transforming 3D into 2D. Think of a cube in 3D; with the projection transform, the points near the far plane come closer together, so the vertices which define the back of the cube (closer to the far plane) also become closer together and appear smaller. When these vertices are drawn on the screen, this tranformation gives the illusion that the back of the cube is smaller than the front and therefore farther. I wish I could explain further, but I think the answer to @kshen’s question could help complete my intuition. How do we determine the depth of each vertex? Do we save the depth as a separate variable associated with the coordinate [x/w, y/w,, 1]^T?