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Unit Cube to Frustum

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8 replies to this topic

#1caibbor  Members

Posted 17 December 2012 - 04:02 PM

I've found countless threads, articles, etc about this topic, but I'm not doing something right. I can create a view frustum but it isn't on the shape of the 'view' (it's much much wider)

I'll explain my process here as best I can without getting too deep into the math. if everything here checks out, I'll look closer at those operations.

steps I take:

1.) create a unit cube (8 vertices) with these bounds:

min/max x: -0.5f to 0.5f
min/max y: -0.5f to 0.5f
min/max z: -0.1f to -1.1f

(if z ranges from positive to negative, the frustum becomes more like an hour glass)

2.) invert my projection matrix
3.) multiply each of my cube's vertices by this inverted projection matrix
4.) ...
5.) profit

I don't know how to apply the view resolution like 800x600 because the thing is already pretty big at this point, with the smallest face of the frustum (the screen) being slightly larger than the actual screen space.

Edited by caibbor, 17 December 2012 - 06:42 PM.

#2santa01  Members

Posted 17 December 2012 - 04:59 PM

Is it really related to OpenGL? Also its not clear what you are trying to do. Are you trying to apply a perspective projection to unit cube so it'll look like a frustum or are you trying to implement a perspective projection itself but transformation gives you an invalid aspect ratio for 800x600 viewport?

#3caibbor  Members

Posted 17 December 2012 - 06:41 PM

it might fit in the Math section better, I just figured I'm using opengl-style matrices as opposed to any other, and perspective/projection is more of a computer graphics thing than mathematics, so... I'm not sure.

I am trying to apply a perspective projection to a unit cube so that it becomes a view frustum, for view frustum culling in my octree. I'm sorry I forgot to mention it's a "view frustum" in the title - editing it now.

edit: not sure I can change the title of the thread.

Edited by caibbor, 17 December 2012 - 06:42 PM.

#4Hodgman  Moderators

Posted 17 December 2012 - 11:19 PM

1) Should be using verts of x/y/z = +1/-1, not +0.5/-0.5. Also, I don't know where -0.1/+1.1 come from...

What values are you using for w?

#5caibbor  Members

Posted 18 December 2012 - 10:32 AM

I figured that +1/-1 wouldn't be a unit cube.. it would be a unit*2 cube

and 0.1 to 1.1 because, like I said, if I use +1/-1 on the z, the nature of the perspective matrix continues to project the cube if it goes behind the camera, makign it look like an hour-glass

(my Z axis is up/down)

using +1/-1 on the z:

using -0.1/-1.1 on the z:

all Vec3's when multiplied by a 4x4 matrix assume a w of 1.

But, it seems I am inverting my projection matrix incorrectly, as discussed later in the conversation here: http://www.gamedev.net/topic/635876-bottom-row-of-4x4-matrix/

Edited by caibbor, 18 December 2012 - 11:23 AM.

#6caibbor  Members

Posted 18 December 2012 - 07:44 PM

update: fixed up and confirmed my perspective invert function is working properly. although with -1/1 bounds on all axes like you mentioned, I'm still getting this hour-glass shaped thing.

#7Hodgman  Moderators

Posted 18 December 2012 - 08:01 PM

D3D and GL each have different types of projection matrices, due to the fact that they each define "Normalized device coordinates" (NDC) differently. After projection (and perspective division, etc), you end up with points in NDC-space, which are then transformed to view-port space, and drawn as pixels.

In GL, NDC is a "unit cube" from -1 to 1 in every axis.
In D3D, NDC is -1 to 1 in x and y, but 0 to 1 in z.

Because of this difference, D3D and GL require slightly different matrices, in order to correctly transform your input vertices into the right kind of so-called "unit cube"

With your results, where negative z values cause a kind of "backwards projection", it sounds like you're using a D3D-style projection matrix? -- in which case, 0/1 for z should give the correct results.

Edited by Hodgman, 18 December 2012 - 08:02 PM.

#8caibbor  Members

Posted 18 December 2012 - 08:48 PM

I'm running Linux Mint. This is OpenGL, I assure you.

I am, however, using my own 4x4 matrix implementation. i've used libraries like glu as references when implementing these, so they should have identical functionality. I'm not using fixed-functionality pipeline, which is why I wrote this library.

Edited by caibbor, 18 December 2012 - 09:01 PM.

#9caibbor  Members

Posted 18 December 2012 - 09:36 PM

even this exaple uses -0.5/0.5 on x and y, and 1/10 as default values on the frustum:

http://www.songho.ca..._transform.html ( scroll all the way to the bottom, look at the image and it's glFrustum() call ).

running this program, it doesn't let you go below 1 for z-near.

Edited by caibbor, 18 December 2012 - 09:37 PM.

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