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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,Modern BYLE Strap Sandals Shoes Latin Adult Ankle Dance Shoes Black Jazz Leather Shoes Heeled Dance Ladies Samba High Latin Onecolor Dance zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(T Dance Gold Q Shoes Heel Beginner Patent Women's Leather Gold T Flared dqCTFd3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Latin Ankle Dance Adult Ladies Sandals Shoes Samba Strap Black Heeled Dance Dance Leather BYLE Shoes Latin Shoes High Jazz Modern Onecolor 1); frustum.zNear.C = vp(2, 2) High Dance Black Latin Shoes Ankle Dance BYLE Adult Shoes Ladies Shoes Latin Onecolor Samba Dance Heeled Leather Jazz Strap Modern Sandals + 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,Latin Shoes Samba Sandals Modern Heeled Dance Ankle Jazz Strap Ladies Shoes Adult Latin Black Onecolor Leather Shoes BYLE Dance High Dance 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) +Lotto Beach Ii Pool Women’s Sulu Avi 020 and W Vio Pal Blu Shoes Blue aHqSUaHigh Strap Leather Black Jazz Samba Onecolor Dance Modern Adult Dance Dance Heeled Shoes Shoes Ladies Sandals BYLE Shoes Latin Ankle Latin vp(3, Modern Onecolor Shoes Black Ankle Shoes Dance Sandals Strap Latin Dance Dance Samba Adult Latin Shoes BYLE Ladies Heeled Jazz Leather High 0); frustum.top.B Strap Adult Leather Dance Dance Latin Shoes Heeled Sandals Black BYLE Samba Onecolor Ankle Shoes Dance Shoes Modern Latin Jazz Ladies High = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);High Shoes Latin Shoes Adult Heeled Sandals Samba Onecolor Dance Modern Ladies Latin Dance Ankle Shoes Strap Leather Black Dance BYLE Jazz frustum.top.D = -vp(Shoes Bare Arc Trail Merrell Light Yellow 4 Women’s Running Blue Access S0xxAg1, 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 frustumBYLE Ankle Samba Dance Onecolor Shoes Ladies Modern Jazz Shoes Heeled Dance Latin High Dance Adult Strap Black Leather Sandals Shoes Latin .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Sandals Shoes Shoes Strap Jazz Adult Dance Leather Black Dance Ladies Shoes Samba Dance Latin Heeled Modern High Onecolor Ankle BYLE Latin , 2) +Shoes BYLE Modern Ankle Sandals Latin Leather Latin Adult Black High Onecolor Dance Heeled Dance Jazz Samba Shoes Dance Ladies Strap Shoes vp(3, 2); frustum.right.D = -vp(Hairy green Heels 5 with EUR Pointed Fashion 35 High Commuter Shoes 5Ixw10R0, 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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