Where does the matrix P come from? Is it just to force the homogeneous coordinates to give us the desired result?
cupoftea
Why do we throw out the third component after the homogeneous divide?
keenan
@merc You can certainly think of it this way: as just a way to implement perspective projection, using the standard 4x4 matrices and homogeneous interpretation of vectors that's available in the standard rasterization pipeline. If you want a deeper view of the relationship between perspective projection and homogeneous coordinates, take a look at projective geometry.
keenan
@cupoftea Because it's always 1, and hence doesn't give you any useful information. ;-). In other words, you just want the projected 2D x and y coordinates. In reality you'll also need a depth value, in order to handle occlusion; if you want a bit more realistic discussion of what happens in the rasterization pipeline, check out this link. We'll talk about some (but not all) of this in a later lecture.
Sleepyhead08
Is there any specific reason we need a 4x4 matrix for this, or is it just because that's the system we're working in? Because it seems like the 4th term in the vectors don't do anything.
Where does the matrix P come from? Is it just to force the homogeneous coordinates to give us the desired result?
Why do we throw out the third component after the homogeneous divide?
@merc You can certainly think of it this way: as just a way to implement perspective projection, using the standard 4x4 matrices and homogeneous interpretation of vectors that's available in the standard rasterization pipeline. If you want a deeper view of the relationship between perspective projection and homogeneous coordinates, take a look at projective geometry.
@cupoftea Because it's always 1, and hence doesn't give you any useful information. ;-). In other words, you just want the projected 2D x and y coordinates. In reality you'll also need a depth value, in order to handle occlusion; if you want a bit more realistic discussion of what happens in the rasterization pipeline, check out this link. We'll talk about some (but not all) of this in a later lecture.
Is there any specific reason we need a 4x4 matrix for this, or is it just because that's the system we're working in? Because it seems like the 4th term in the vectors don't do anything.