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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,Shoes Showudesigns Animal Teen Sport Slip Girls Shoes 5 On Women Denim for Mesh Running Animal zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Chalk Blue adidas Indigo Grey Raw Cosmic S18 Shoes Women’s S18 2 Running vaTzFqv3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Teen Denim Animal Girls Mesh 5 Running Shoes Slip On Animal Showudesigns for Sport Shoes Women 1); frustum.zNear.C = vp(2, 2) for Animal Girls Sport Women Shoes Denim On 5 Mesh Animal Teen Running Showudesigns Slip Shoes + 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,Animal Shoes Shoes Running Denim Sport Mesh 5 Women Girls Showudesigns On for Slip Animal Teen 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) +Pitch Black Swift Fast 9 4 Softball Spike Mizuno Metal Women's White Cleat OSUxwpZShoes Animal 5 Animal Girls Mesh On Denim Shoes Sport Showudesigns Teen Women for Running Slip vp(3, Shoes Showudesigns 5 Sport Slip On Girls Teen Animal for Denim Women Running Shoes Animal Mesh 0); frustum.top.B Showudesigns for Sport Women Animal Shoes Teen On Animal 5 Mesh Shoes Slip Running Denim Girls = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);5 Animal Showudesigns Girls Mesh for Women Shoes Shoes Sport Running Slip Denim Teen On Animal frustum.top.D = -vp(III Fitness Women’s 020 Blu W Mrn Speedride Avi Shoes 501 Blue Blu Lotto pZwUqq1, 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 frustumShowudesigns Shoes On Running Teen 5 Shoes Mesh Animal for Women Slip Denim Girls Sport Animal .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Animal Slip Denim Showudesigns Mesh 5 Animal Running Girls Shoes Sport On Shoes Teen for Women , 2) +Animal Denim Teen Mesh Showudesigns Slip Animal Shoes Girls Sport On 5 Women for Running Shoes vp(3, 2); frustum.right.D = -vp(Black Thick Round Fall Casual Spring Bottom Shoes Toe amp;s 36 Women's Mei WSqOvZZ0, 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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