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OpenGL Frustum Planes Extraction: I just don't get it

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I'm starting to feel like I'm the first person to ever really try to extract the frustum planes from the view and projection matrices... This can't possibly be true so there must be something very fundamental that I'm missing..... right? First of all it seems like just about every article on this subject is for OpenGL and the few which are for DirectX are conflicting... if you look at these two DirectX examples, they have a similar idea... but they are also very different at the same time plane extraction How do I get the viewing frustum? I just don't know what to make of it... I've tried the code in both articles and I just can't seem to get it to work at all... I'm actually having trouble understanding how any of these algorithms CAN work... in all the articles I read (including the OpenGL ones), all of the information about the D component of the planes is extracted from the bottom row of the matrix... in all of the tests I've run, my View*Projection matrix has all zeros in that last row... which means that no matter what I do, all of the D's are zero here's an example matrix I got:
[1.73205	0		0		0	]
[0		1.001		1		0	]
[-1.73205	-0.1001		0		1.29904	]
[0		0		0		0	]
And here's the code I use to make the matrices:
	D3DXMATRIX matWorld;
	d3dDevice->SetTransform(D3DTS_WORLD, &matWorld);

	//D3DXMATRIX matView;
	D3DXVECTOR3 vEye( 0.0f, 0.0f, 0.0f );
	D3DXVECTOR3 vAt( 0.0f, 0.0f, 1.0f );
	D3DXVECTOR3 vUp( 0.0f, 1.0f, 0.0f );
	D3DXMatrixLookAtLH( &matView, &vEye, &vAt, &vUp);
	d3dDevice->SetTransform( D3DTS_VIEW, &matView );

	D3DXMATRIX matProj;
	D3DXMatrixPerspectiveFovLH( &matProj, D3DX_PI/3, 4/(float)3, 0.1f, 100.0f );
	d3dDevice->SetTransform( D3DTS_PROJECTION, &matProj );

What in the heck am I forgetting?... maybe I'm not supposed to multiply the matrices in the order that I do (View * Projection)? maybe this algorithm doesn't return the planes in world space... but that still doesn't explain why the D's are always zero

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Yes, the equations for DirectX and OpenGL are different, owing to the fact that one is right-handed and one is not. I believe a simple transposition of the matrices will correct the differences.

Even with the OpenGL/DX thing cleared up, I remember it took me a bit of work to get the correct matrices in and the right clip planes out. Keep trying and you'll get it.

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The plan extraction article ( is definetly correct.

The View * Projection is also correct.

It looks like you are calculating the view and proj matrices correctly.

And the paper you linked does return the frutum in world space.

Maybe you're messing up somewhere else. If you would like me to send you a frustum class just PM me and Ill send you one so that you can compare and see if you catch anything.

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I finally figured out what I was doing wrong!

I was using the D3DXMATRIX structure (SDK 8.0) and to get at the elements of the matrices I was using its overloaded () operator

from the sdk

// access grants
FLOAT& operator () ( UINT Row, UINT Col );
FLOAT operator () ( UINT Row, UINT Col ) const;

by "access grants" I assumed they meant they would grant me access to the elements... but I can't really figure out what they do

here is a View*Projection matrix:

[-1.81066 0 0 0 ]
[0 2.41421 0 0 ]
[0 0 -1.002 -1]
[0 -2.41421 -0.1002 0 ]

And here is that same matrix through the eyes of the () operator:

[2.41421 0 0 0 ]
[0 -1.002 -1 0 ]
[-2.41421 -0.1002 0 1.81066 ]
[0 0 0 0 ]

I'm wondering if this is a bug that has long been fixed by newer versions or if this has some legitimate purpose...

Anyhow... Thanks for your responses guys... much appreciated

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This is three weeks old (sorry, almost necro :-) but the reason you got that bug was that you used indices from 1 through 4; the () operator wants values from 0 through 3. You can tell this is the case, because the upper-left 3x3 matrix you got out is the same as the lower-right 3x3 of the input matrix.

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I have also never quite understood the way the frustum planes are exracted from the view and projection matrices. I propose a simpler approach. Maybe this is already a well know one, but I have not seen any tutorial using it). I figured this one out myself and it is so much simpler.

Here is the technique,

you already know the nearZ, farZ and fov (horizontal)and aspect (width / height) of your view volume.

From this information, using simple trignometry , we can compute the camera space coordinates of the 8 corners of the frustum. Compute these once every time you update any FOV related settings and store them.

Then each frame, transform each of these points to world spcae, using your world transform matrix. Once in world space, use these points to compute the 6 planes! (computing a plane from 3 points is easy enough)

I am attaching the code to do this. It is not compilable as is, (as it uses other classes as well and is a work in progress) but will serve to explain the concept!


[Edited by - AQ on September 25, 2004 10:40:29 AM]

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I used the frustum tut from ravensoft as a result of reading this thread a few weeks ago. I replaced the frustum plane comp i was using with that one and I am very happy with the results. I highly recommend that tutorial to everyone.

AQ your concept sounds very interesting. when I clicked on the link the code sample doesn;t show how you build your planes. would be interesting to see that. I think that's pretty cool that you have developed your own view frustum technique.

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Another approach is to treat the frustum planes as 2D rays, like consider from top view i.e. the XZ plane (if your camera is at origin and facing along the positive x-axis):

the left plane is equivalent to a ray:

(cos (fov/2), 0, sin(fov/2))

then any point u want to test as inside or outside the frustum:

point -= camera; //translate to frustum space
//unrotate point if necessary

dPl = dot(leftPlane, xAxis);
dPt = dot(point, xAxis);

if (dPl < dPt) //point is "below" the left plane ray
if (dot (leftPlane, point) > 0)
//point is within left/right planes

Then you can do an && with testing on the XY plane for top and bottom planes (left view).
This way requires testing of only 2 planes (left and top) and deal with rays rather than planes (which i find easier anyway), and for near and far clip you can just test if (near < point.x < far). Also this way you dont have to worry about transforming the frustum to world space, it is easier and faster to untransform the point/volume being tested to frustum-relative space. Atleast, I found it to be so.

The only snag is it screens out coplanar points, but you can do a quick prelim test for that easily (dot(plane, point) == 1).
Can anyone spot any problems?

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