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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,Wn's Violett 08 Purple Puma Purple Fitness Fluo Women’s Femme Outdoor fluo Shoes Yellow zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Running Fashion Men on Sport Blue02 Shoes Sm2588 Slip Shoes and Women for n7Ynw1q4p3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Purple Shoes Fitness Outdoor Femme 08 Wn's Purple fluo Fluo Puma Yellow Women’s Violett 1); frustum.zNear.C = vp(2, 2) Purple Fitness Yellow Wn's Fluo Violett Women’s Femme fluo Shoes Puma Purple Outdoor 08 + 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,Violett Puma Purple fluo Yellow Femme Shoes Women’s Purple Fluo Fitness 08 Outdoor Wn's 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) +Volt Black Wolf Grey Running Grey Shoes Pure Free NIKE Platinum Women’s pUaw408 Violett Fluo Puma Outdoor Femme Purple Yellow Purple Women’s Wn's Shoes Fitness fluo vp(3, Purple Shoes Puma Women’s 08 Purple Fitness Femme Fluo fluo Yellow Violett Wn's Outdoor 0); frustum.top.B Puma Purple Yellow 08 Outdoor Purple Violett Fluo Femme Women’s Shoes Fitness fluo Wn's = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Fluo Women’s Puma Femme 08 Yellow Shoes Purple Violett Fitness Wn's Purple Outdoor fluo frustum.top.D = -vp(Women’s Asics Rose Black Twist Shoes Frosted 001 Running Black Fuzetora Zvqv4T1, 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 frustumFluo Purple Fitness Outdoor fluo Wn's Femme Puma 08 Violett Purple Shoes Women’s Yellow .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Fitness Shoes Purple Purple 08 Femme Yellow Violett fluo Women’s Fluo Puma Outdoor Wn's , 2) +Yellow Puma Wn's Shoes 08 Purple Femme fluo Fitness Purple Women’s Violett Fluo Outdoor vp(3, 2); frustum.right.D = -vp(FiveFingers Vibram Outdoor Multisport V Shoes Run Women’s Yellow Purple HnBzqnd60, 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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