Hi all,
Currently, I'm very interested in 3D to 2D projection, but I'm quite new to using matrices with this calculations. The question I have now is as following:
When I try to figure out a way to do 3D projection, I first tried to do 2D to 1D projection to get the concept right. That seems very simple: let the origin be the 'center of projection' O(0, 0), place the 1D projection plane on a certain positive x value and every point (for simplicity only in x positive) can be projected unto the projection plane by drawing (calculating) a line to through this point and the origin. Then find the y value with the x of the projection plane. See the image below:
The calculation for this looks like:
P * A = X and then do homgeneous division.
An example of this with 3D projection is:
This looks all fine, but now my question is... Most 3D perspective projection matrices take into account FOV, perspective angle, far/near plane etc. Such a matrix looks like:
Why isn't my 'simple' matrix enough, and what exactly does this real matrix do (better) relative to my matrix? If some one could explain this 3d projection without a matrix (just using regular algebra) would be very helpful! That way I can better understand whats going on exactly. If possible use a 2D to 1D example for simplicity.
Thanks!
Currently, I'm very interested in 3D to 2D projection, but I'm quite new to using matrices with this calculations. The question I have now is as following:
When I try to figure out a way to do 3D projection, I first tried to do 2D to 1D projection to get the concept right. That seems very simple: let the origin be the 'center of projection' O(0, 0), place the 1D projection plane on a certain positive x value and every point (for simplicity only in x positive) can be projected unto the projection plane by drawing (calculating) a line to through this point and the origin. Then find the y value with the x of the projection plane. See the image below:
The calculation for this looks like:
P * A = X and then do homgeneous division.An example of this with 3D projection is:
This looks all fine, but now my question is... Most 3D perspective projection matrices take into account FOV, perspective angle, far/near plane etc. Such a matrix looks like:
Why isn't my 'simple' matrix enough, and what exactly does this real matrix do (better) relative to my matrix? If some one could explain this 3d projection without a matrix (just using regular algebra) would be very helpful! That way I can better understand whats going on exactly. If possible use a 2D to 1D example for simplicity.
Thanks!