OK.

So hello and welcome for our computer graphics lecture.

And today we will speak about another important part

of the rendering pipeline.

And these are transformations.

So when doing rendering, as you will see today

and in the next lectures, we will

do lots of geometric transformations on points.

So we will interpret points in different coordinate systems.

And it's a long way from a point that

is defined somewhere in a local coordinate system

up to the moment that it's on the screen

and directly has a pixel address.

And the different phases, the different steps

of this pipeline, we will speak about later on.

Today we will speak about the theory of these transformations

and how we can describe these transformations

in a nice and elegant way that is not really redundant

but supports everything that we will need during

or within our rendering pipeline.

And yeah, so we will start with a simple or rather simple

class, subclass of transformations.

These are affine transformations.

We will see what different steps we can describe by these.

We will then have a look at homogeneous coordinates.

Some of you probably already saw these.

And we'll then go to a more interesting class

of transformations.

These are projective transformations.

These will be required to also represent perspective, which

is, as you will see, not that simple.

And since they are a very important subpart,

and there are many different ways to describe them,

we will have a closer look in particular on rotations.

OK, but first of all, let me give you

a little introduction about the different phases where

we will need transformations and what types of transformations

will be applied there.

So in our rendering pipeline, we first of all

have these steps that describe what we will call the modeling

transformation.

The idea of the modeling transformation

is the following.

We have a world coordinate system

that we can define somehow.

So we say, OK, now this is our origin, here, my hand.

This is the x.

This is the y.

And this is, no, this is x.

This is y.