<p>The mapping from NDC space to screen space is orthographic.</p>

<p>The x is mapped linearly from [-1, 1] to [0,viewport width], same with y and viewport height.</p>

<p>This mapping happens after the projection matrix has been applied and the divide by w happened. </p>

CC BY-SA 3.0
2017-03-14T10:08:22.523Z
So the divide by w brings the 4d coordinates to 3d and then the 3d points are orthographically projected to 2d? So a perspective projection really also encompasses a final orthographic projection?
transporter_room_3
CC BY-SA 3.0
2017-03-14T10:01:29.640Z
2017-03-14T10:01:29.640Z
ratchet freak
<p>I don't completely understand the last part of the MVP matrix (projection).</p>

<p>In orthographic projection we simply scale the view volume into the default view volume (+-1 on all axis).</p>

<p>In perspective projection we scale and skew the view frustrum into the default view volume (+-1 on all axis) which causes non-uniform foreshortening giving the appearance of perspective that we're used to.</p>

<p>So now, regardless of which type of projection we have used, we have the default viewing volume (+-1 on all axis). So how do we get from this cube to an image on the screen?</p>

<p>I understand that we need this volume for the z-buffer. But how are points (anywhere in this volume) finally transformed from 3d to 2d and is it the same procedure for orthographic projection as it is for perspective projection?</p>

<transformations><projections><perspective>
Getting from the default view volume to an image on the screen
transporter_room_3
# Getting from the default view volume to an image on the screen

(Asked by: username_0 on 2017-03-14)

I don't completely understand the last part of the MVP matrix (projection).

In orthographic projection we simply scale the view volume into the default view volume (+-1 on all axis).

In perspective projection we scale and skew the view frustrum into the default view volume (+-1 on all axis) which causes non-uniform foreshortening giving the appearance of perspective that we're used to.

So now, regardless of which type of projection we have used, we have the default viewing volume (+-1 on all axis). So how do we get from this cube to an image on the screen?

I understand that we need this volume for the z-buffer. But how are points (anywhere in this volume) finally transformed from 3d to 2d and is it the same procedure for orthographic projection as it is for perspective projection?

**Tags:** transformations, projections, perspective


---

## 1 answers

### Answer by username_1 on 2017-03-14. Score: 2 | Accepted answer

The mapping from NDC space to screen space is orthographic.

The x is mapped linearly from [-1, 1] to [0,viewport width], same with y and viewport height.

This mapping happens after the projection matrix has been applied and the divide by w happened.

> **Comments:**
> **username_0**: So the divide by w brings the 4d coordinates to 3d and then the 3d points are orthographically projected to 2d? So a perspective projection really also encompasses a final orthographic projection?  

---

