OK.

So welcome for our computer graphics lecture.

Sorry for the delay.

But now we have a completely fresh computer.

At least we are with this respect on the safe side.

So we are, or last Thursday, I spoke about clipping.

And yeah, clipping is a problem.

Or the problem that is handled by clipping

is that we typically have a rectangular view

pod, a rectangular window, which we draw our objects into.

And now it, of course, regularly happens

that these objects are partially outside this window

and now have to be clipped.

That means everything outside the window

needs to be cut off before it is rendered.

And so we saw an algorithm for clipping of lines.

And yeah, as I said, of course, the part

that is more interesting for us is not how to clip lines,

but to clip polygons.

And now you might say, OK, a polygon

is just a set of edges.

So if I know how to clip lines, I

know how to clip polygons.

But in fact, that's not the case.

So if we look at this example here,

we have this triangle, P1, P2, P3.

And P1 is outside of our window.

And now the point is that it is not enough to clip these lines.

But instead, we are not interested in the edges only,

but also in the interior.

And to describe the interior correctly after this clipping,

we need to generate this object.

And this object now has four vertices.

And now we get a quadrilateral.

And this is the clipped version of that triangle.

And we are not only interested in this edge and this edge,

but in fact, this new edge here also

has to be generated to get a closed loop again.

Now for that example, you might say,

OK, that's still very, very simple.

But that can also more difficult cases happen.

Yeah, so look at this example here.

Now here, it really becomes more complicated.

And this quadrilateral here becomes something

with eight vertices, I think.

And in this example, now something even more difficult

happens, because if we only clip the lines, what remains

is only this part here.

And now we have to add these two edges so that we get back

a closed polygon again.