I have seen that calculation before, so I am definitely interested to see how its derived since it very much confused me.
jacheng
How does this matrix differ from its effects from the matrix on the previous slide?
ceviri
I think it would be nice to have a comparison image between the perspective/orthographic transforms here.
keenan
@jacheng The matrix on the previous slide performs an orthographic projection, whereas the one on this slide performs a perspective projection. Basically by choosing different initial "shapes" for your view frustum (either a box with parallel edges, or a box with edges along rays from the eye) you get different projections when you warp that box onto the standard box $[-1,1]^3 \subset \mathbb{R}^3$.
keenan
@ceviri Yeah, totally agree that there are some great opportunities for visualization here. For instance, you could really visualize the view frustum being warped into the normal coordinates, and warping some object along with it! Maybe you can create such a visualization? :-)
tbloch
What do l, r, t, and b refer to here, since the left, right, top, and bottom of the frustum are no longer constant (as in the orthographic case)?
edit: from the link at the bottom, it looks like they are the left, right, top, and bottom of the frustum at the near plane.
I have seen that calculation before, so I am definitely interested to see how its derived since it very much confused me.
How does this matrix differ from its effects from the matrix on the previous slide?
I think it would be nice to have a comparison image between the perspective/orthographic transforms here.
@jacheng The matrix on the previous slide performs an orthographic projection, whereas the one on this slide performs a perspective projection. Basically by choosing different initial "shapes" for your view frustum (either a box with parallel edges, or a box with edges along rays from the eye) you get different projections when you warp that box onto the standard box $[-1,1]^3 \subset \mathbb{R}^3$.
@ceviri Yeah, totally agree that there are some great opportunities for visualization here. For instance, you could really visualize the view frustum being warped into the normal coordinates, and warping some object along with it! Maybe you can create such a visualization? :-)
What do l, r, t, and b refer to here, since the left, right, top, and bottom of the frustum are no longer constant (as in the orthographic case)?
edit: from the link at the bottom, it looks like they are the left, right, top, and bottom of the frustum at the near plane.