Hello, and welcome for our computer graphics lecture.

So we are right now in the process

of trying to understanding perspective.

So what I told you last time, so OK, let's start the other way

around maybe.

Perspective means we have a world in 3D,

and now we want to transform this into a 2D image.

And typically effects now occur.

For instance, objects further away

get smaller on the image and stuff like that.

And we are looking into this process.

How can we project the three dimensional world

onto our 2D image?

And in fact, they are two different.

They're not fundamentally different.

In fact, they are the same in homogeneous space.

But two different ways to do such a projection that

are also used in practice.

There are many more, by the way.

These are the ones we will look at.

And this is orthographic and perspective projection.

And orthographic just means that we

take the three dimensional world and project it

onto our image by a parallel projection.

This gives us images like this.

And it has the property that parallel lines always

remain parallel.

And you might remember that this means it's an affine mapping.

And the alternative is what is a real perspective projection.

That's an image like a camera generates it,

or like the eye generates it, the human eye.

And that's a perspective projection.

And that's a projection where objects

are projected onto the image plane using point projection

or central projection.

So every point here is projected onto this plane

by generating a line through the eye and the point.

And where it intersects the image plane,

that's the point where it's projected to.

And as I said, these two are, in fact, the same.

So if I take this point and put it to infinity

and move it towards infinity, then you

get a parallel projection.

So it's not fundamentally something different.

It is very similar.

OK, and both of these projections

define what we call a view volume.

So the view volume contains all points

in our world that are projected onto the image.

So for the orthographic projection, this is a box.