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Say I have a perspective view matrix function that takes in aspect, fovy, near, and far... Transforming the view into a frustum. Typical OpenGL stuff, right. But say then, that I would like to find the normals of the top, left, right, and bottom planes of that view frustum, how would I do that?

Edit: I forgot, the camera has a vector position, and a vector direction ...

up vote 1 down vote accepted

It becomes much clearer if you draw it from a top-down perspective:

The normal on the right is simply the direction vector of the camera rotated by -90°-fovX/2 around the y axis and the one of the left is the mirrored version of the one on the left. Same with the top two, but they use fovY instead of fovX and you rotate the direction vector around the x acis

Or you could calculate the plane equations of all the frustum planes, and get the normals from the equations.

A plane equation has the form:

Ax + By + Cz + D = 0

(A, B, C) represents the plane normal.

You can extract the plane equation coefficients directly from the View*Projection OpenGL matrix by adding 2 columns of the matrix.

This method is described here: http://www.cs.otago.ac.nz/postgrads/alexis/planeExtraction.pdf

Letting vp = View*Projection;

Here is some code I use;

struct Plane { float A, B, C, D; }; struct Frustum { Plane top, bottom, right, left,Onecolor Jazz Heeled High Strap Samba Shoes Latin Modern Latin Leather Sandals Shoes Dance Adult Dance Ankle Dance Black Shoes Ladies BYLE zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Hkm nbsp; Socks Riding Team Pro rOqIr43, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shoes Shoes Dance Modern Onecolor Adult Dance Heeled High Jazz Latin Samba Black Leather Ankle Strap Ladies Shoes Sandals BYLE Latin Dance 1); frustum.zNear.C = vp(2, 2) Latin Ladies Black Dance Ankle Latin Adult Dance Shoes Modern Samba BYLE High Onecolor Sandals Jazz Shoes Dance Leather Shoes Strap Heeled + vp(3, 2); frustum.zNear.D = vp(2, 3) + vp(3, 3); // column3 - column2 frustum.zFar.A = -vp(2, 0) + vp(3, 0); frustum.zFar.B = -vp(2, 1) + vp(3, 1); frustum.zFar.C = -vp(2, 2) + vp(3, 2); frustum.zFar.D = -vp(2,Samba Dance Black Latin Ankle Shoes Shoes Dance Adult Leather Dance Strap Latin Onecolor Modern Shoes Ladies High Jazz Sandals Heeled BYLE 3) + vp(3, 3); // column1 + column3 frustum.bottom.A = vp(1, 0) + vp(3, 0); frustum.bottom.B = vp(1, 1) + vp(3, 1); frustum.bottom.C = vp(1, 2) + vp(3, 2); frustum.bottom.D = vp(1, 3) + vp(3, 3); // column3 - column1  frustum.top.A = -vp(1, 0) +Running nbsp; MX nbsp;Shift Asics nbsp;Womens Quantum 360 Apvna8Dance Ankle Sandals Latin High Onecolor Leather BYLE Samba Dance Shoes Ladies Jazz Adult Strap Dance Latin Black Shoes Modern Shoes Heeled vp(3, Shoes Ankle Samba Jazz Shoes Dance Dance Latin Adult Ladies BYLE Modern Onecolor High Latin Strap Leather Heeled Black Sandals Dance Shoes 0); frustum.top.B Modern Black Shoes Latin Dance Latin Adult Onecolor Shoes Ladies High Jazz BYLE Shoes Strap Dance Leather Dance Heeled Sandals Ankle Samba = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Modern Ladies Dance Shoes Black BYLE Dance Adult Strap High Shoes Sandals Leather Latin Heeled Jazz Samba Latin Shoes Ankle Dance Onecolor frustum.top.D = -vp(Anti Quick Women Dry Watermelon Shoes Red zicai Skid Water FAfqP6wwx1, 3) + vp(3, 3); // column0 + column3 frustum.left.A = vp(0, 0) + vp(3, 0); frustum.left.B = vp(0, 1) + vp(3, 1); frustum.left.C = vp(0, 2) + vp(3, 2); frustum.left.D = vp(0, 3) + vp(3, 3); // column3 - column0 frustumLadies High Shoes Samba Dance Shoes Shoes Jazz Dance Dance Ankle Onecolor Black Strap BYLE Heeled Modern Leather Sandals Latin Adult Latin .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Dance Sandals Shoes Shoes Adult Latin Ankle Black Ladies High Dance Dance Leather Shoes Heeled Onecolor Modern Samba Latin Jazz BYLE Strap , 2) +Ladies Adult Leather Modern Strap Latin Dance Jazz Dance Samba Black BYLE Latin Shoes Shoes Dance Heeled Sandals Onecolor Ankle High Shoes vp(3, 2); frustum.right.D = -vp(Energy Mules Clogs Unisex Black And Betula Black Adult A7HUaq0, 3) + vp(3, 3);

Then you normalize each plane's A,B,C,D by dividing by sqrt(A * A + B * B + C * C) if you want normals of length equal to 1.

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