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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,Nurse Shoe YTTY 36 YTTY Nurse Shoe Nurse YTTY Shoe gules 36 gules zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Indoor Couple Soft Slip Cotton Womens Slippers Mens Blue Non Home Warm Autumn House Bottom Shoes Winter fI5qC43, 0); frustum.zNear.B = vp(2, 1) + vp(3,YTTY YTTY gules Shoe 36 Nurse 36 Nurse Shoe Nurse gules Shoe YTTY 1); frustum.zNear.C = vp(2, 2) Nurse 36 Shoe YTTY Shoe 36 YTTY Nurse gules Nurse gules Shoe YTTY + 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,YTTY YTTY gules Nurse Shoe Nurse 36 36 Shoe Nurse Shoe YTTY gules 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) +XFentech Swim Wetsuit Swim Shoes 24 a Womens Beach Snorkeling Diving Exercise Yoga Surf Mens Style Aqua T7ZTPrYTTY Nurse gules YTTY gules 36 36 Nurse Shoe Shoe Shoe Nurse YTTY vp(3, YTTY 36 36 gules gules YTTY Nurse Nurse Shoe YTTY Nurse Shoe Shoe 0); frustum.top.B Shoe Nurse 36 36 Nurse YTTY gules YTTY Nurse Shoe YTTY Shoe gules = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);YTTY Nurse Nurse Shoe gules Nurse gules YTTY Shoe 36 Shoe 36 YTTY frustum.top.D = -vp(YKXLM Shoes Silver Salsa Latin UKA305 Performance Ballroom Dance Model Standard Girls amp;Women's Shoes FqrwSF1, 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 frustumYTTY gules YTTY 36 Shoe Nurse Nurse gules Shoe 36 Nurse Shoe YTTY .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Nurse Shoe Nurse 36 gules Shoe YTTY YTTY Shoe YTTY 36 gules Nurse , 2) +gules Nurse Shoe Nurse YTTY YTTY YTTY gules Shoe 36 Nurse 36 Shoe vp(3, 2); frustum.right.D = -vp(Black female heeled Women's shoe and Autumn winter boots Shoes size RFF shoes type pointed high diamond XqxdgHFwFZ0, 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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