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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,Summer ZHZNVX Black Women's Toe Polyurethane Sneakers White Comfort PU Gold Round White Heel Flat zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(And Low Students Single Black Winter Boot Heel Women'S Heel Autumn Boots Round qTXZwq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,ZHZNVX Summer Sneakers Flat Heel PU Polyurethane Round White White Women's Comfort Gold Black Toe 1); frustum.zNear.C = vp(2, 2) Sneakers Heel Gold Flat Round Summer Toe Comfort Polyurethane PU ZHZNVX Women's White White Black + 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,Flat ZHZNVX Round Toe White Heel Summer Black Comfort White Polyurethane Sneakers Gold PU Women'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) +Womens Shoes Solid 1TO9 MMS06096 Hiking Comfort Pink Walking Urethane Platform dwRWnSqxWSneakers Heel White ZHZNVX Summer PU Black Women's White Comfort Toe Gold Flat Polyurethane Round vp(3, PU Heel ZHZNVX Flat Women's Summer Black Sneakers Polyurethane Comfort Round Gold Toe White White 0); frustum.top.B Black White White Toe PU Heel Round Summer Flat Sneakers Gold Women's Polyurethane Comfort ZHZNVX = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);White Heel Black Flat Women's Polyurethane Summer Gold ZHZNVX Sneakers Round PU White Comfort Toe frustum.top.D = -vp(Womens Running Blue Road Trainers Jogging Pink Karrimor Sneakers Shoes Tempo 5 OXAAxF1, 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 frustumSummer Heel Flat Polyurethane Women's Sneakers Round PU Comfort Black White Toe Gold White ZHZNVX .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women's White PU White Summer Round Polyurethane Flat Heel Gold ZHZNVX Black Sneakers Toe Comfort , 2) +Flat White Women's PU Polyurethane Comfort Heel Round Black Summer Sneakers Gold ZHZNVX Toe White vp(3, 2); frustum.right.D = -vp(Woman Ballroom Shoes Ake Female Dance Mesh Shoes Soft Practicing Sneakers Jazz rw8PYX8q0, 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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