What about lines that are parallel to the planes? Why can we just ignore them?
chenruis
I think we can ignore them because we are caring about mapping the point p on a designated 2D plane to the representation of \hat{p}? So for arbitrary point p on the plane, as long as the plane does not cross O, the line would be unique. It's possible that lines are parallel to the plane, but a few slides later the slide is only discussing about doing affine transformation on the point p on a 2D plane, and I think that restricts the line cannot be parallel to the plane.
It's just a random thinking, I don't know for sure, too.
ohmygearbox
I find it kind of cool that the homogenous coordinates are also used in other fields like vision and robotics.
What about lines that are parallel to the planes? Why can we just ignore them?
I think we can ignore them because we are caring about mapping the point p on a designated 2D plane to the representation of \hat{p}? So for arbitrary point p on the plane, as long as the plane does not cross O, the line would be unique. It's possible that lines are parallel to the plane, but a few slides later the slide is only discussing about doing affine transformation on the point p on a 2D plane, and I think that restricts the line cannot be parallel to the plane.
It's just a random thinking, I don't know for sure, too.
I find it kind of cool that the homogenous coordinates are also used in other fields like vision and robotics.
Story of drawing 3D on a 2D screen?