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# Extracting 6 Frustum Planes from camera Position, Direction, FOV And Viewing Distance

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6 replies to this topic

### #1Code-R  Members

Posted 15 May 2005 - 11:44 AM

How can this be done?? TIA

### #2scgames  Members

Posted 15 May 2005 - 11:58 AM

Quote:
 How can this be done??
Like this :)

### #3Code-R  Members

Posted 15 May 2005 - 12:35 PM

"from camera Position, Direction, FOV And Viewing Distance", not the MVP matrix. I've googled ;). thanx for the effort anyway!

### #4scgames  Members

Posted 15 May 2005 - 12:48 PM

Got it. You can also do it from the information you have using trig. For this you'll need the fov in both directions, so you'll need to calculate one from the other (horizontal from vertical or vice versa).

The normals to the near and far planes are simply +/- the view direction vector. The distances can be found using your camera position and a little vector math.

The normals for the other planes can be found using the sin and cos of half your horizontal and vertical fov, and your camera's local frame. Then dot the normals with the camera position to find the distances.

Note that the info you mentioned doesn't uniquely determine a frustum - you need a complete local frame, that is, an up or side vector in addition to the direction vector. I assume you have that available.

I've actually written this code before and have it lying around on my hard drive somewhere. If you get stuck on the implementation, let me know and I'll find the code and post it.

### #5Code-R  Members

Posted 15 May 2005 - 01:32 PM

how can i calculate one fov from the other?
TIA

### #6scgames  Members

Posted 15 May 2005 - 02:50 PM

Quote:
 how can i calculate one fov from the other?
Ok, let's see if I remember this...

We'll use the following variable names:

hFov = horizontal fov/2
vFov = vertical fov/2
w = screen width/2
h = screen height/2
d = distance to screen
aspect = w/h

Next, note that:

tan(hFov) = w/d
tan(vFov) = h/d

Let's say we know hFov and we want to find vFov.

tan(hFov) = w/d
(w/d)/aspect = (w/d)/(w/h) = (w/d)(h/w) = wh/dw = h/d = tan(vFov)

Therefore:

vFov = atan(tan(hFov)/aspect)

If we know vFov and we want to find hFov:

tan(vFov) = h/d
(h/d)aspect = (h/d)(w/h) = hw/dh = w/d = tan(hFov)

And:

hFov = atan(tan(vFov)aspect)

So all you need is the aspect ratio and either the horizontal or vertical fields of view. Don't forget to add the factors of 2 back into the equations.

Anyway, I think I got that right - if I made any errors I'm sure someone will point them out.

### #7ptl  Members

Posted 16 May 2005 - 11:34 AM

Extracted from my own code (thats works wells) :


void CFrustum::CalculateFrustum(const CCamera &rCamera)
{
// We need 6 clipping planes for the standard frustum, more the additional planes
// Provided by the user
ClearPlanes();
const vector&lt;CPlane*&gt; &vecUserPlanes = rCamera.GetClipPlanesVector();
m_clipPlanes.reserve(6 + vecUserPlanes.size());

uint32 i, ip;
CMat4x4 matView = ((CCamera&)rCamera).GetViewMatrix();
CMat4x4 matProj = ((CCamera&)rCamera).GetProjectionMatrix();

// Calculate half Width and Height at near plane distance
float fHalfFovTan = tanf(PHSR_DEGREE_TO_RADIAN(rCamera.GetFieldOfView() / 2.0f));
float fNear = rCamera.GetNearZ();
float fHalfW = fHalfFovTan * fNear;
float fHalfH = fHalfW / rCamera.GetAspectRatio();

// Get orientation of the frustum
CVector3 vIn, vLeft, vUp;
vIn = matView.GetIn();
vLeft = matView.GetLeft();
vUp = matView.GetUp();

// Calculate scaled vectors descibing the VF
float fZRatio = (rCamera.GetFarZ()) / rCamera.GetNearZ();
CVector3 kDScaled = vIn * rCamera.GetNearZ();
CVector3 kLScaled = vLeft * fHalfW;
CVector3 kUScaled = vUp * fHalfH;

// Calculate the four near corners
m_vFrustumCorner[0] = kDScaled - kLScaled - kUScaled;
m_vFrustumCorner[1] = kDScaled - kLScaled + kUScaled;
m_vFrustumCorner[2] = kDScaled + kLScaled + kUScaled;
m_vFrustumCorner[3] = kDScaled + kLScaled - kUScaled;

// Deduce the four far corners
for (i = 0, ip = 4; i &lt; 4; i++, ip++)
{
m_vFrustumCorner[ip] = rCamera.GetPosition() + m_vFrustumCorner[i] * fZRatio;
m_vFrustumCorner[i] += rCamera.GetPosition();
}

////
// Calculate clipping planes from corners
////
CPlane *pPlane = NULL;

// Bottom
m_clipPlanes.push_back(new CPlane(m_vFrustumCorner[0], m_vFrustumCorner[4], m_vFrustumCorner[3]));

// Top
pPlane = new CPlane(m_vFrustumCorner[1], m_vFrustumCorner[5], m_vFrustumCorner[2]);
m_clipPlanes.push_back(pPlane);
pPlane-&gt;Reverse();

// Left
m_clipPlanes.push_back(new CPlane(m_vFrustumCorner[0], m_vFrustumCorner[1], m_vFrustumCorner[4]));

// Right
pPlane = new CPlane(m_vFrustumCorner[3], m_vFrustumCorner[2], m_vFrustumCorner[7]);
m_clipPlanes.push_back(pPlane);
pPlane-&gt;Reverse();

// Near
pPlane = new CPlane(m_vFrustumCorner[0], m_vFrustumCorner[1], m_vFrustumCorner[3]);
m_clipPlanes.push_back(pPlane);
pPlane-&gt;Reverse();

// Far
m_clipPlanes.push_back(new CPlane(m_vFrustumCorner[4], m_vFrustumCorner[5], m_vFrustumCorner[7]));

// Add clipping planes provided by the user
for (i = 0 ; i &lt; vecUserPlanes.size() ; i++)
{
// Use copy constructor
m_clipPlanes.push_back(new CPlane(*vecUserPlanes[i]));
}
}



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