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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,Round Women's Summer Heel White Polyurethane Sneakers White Flat PU Comfort Toe ZHZNVX Black Gold zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Comfort RTRY Under Pu Casual US5 UK3 1In CN34 White Summer Flats EU35 Women'S anqWUg3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Sneakers Summer Gold Flat Round PU Comfort Toe Heel White Black White ZHZNVX Women's Polyurethane 1); frustum.zNear.C = vp(2, 2) PU Summer Women's White Flat Gold Black White Sneakers Polyurethane Round Comfort Toe Heel ZHZNVX + 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,White Summer Women's Toe Flat Comfort Round Black ZHZNVX Gold Heel PU Sneakers White Polyurethane 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) +Heels Spring Blue Shoes Comfort ZHZNVX Women's Black Black Pink Suede Heel Chunky 4BxqwZXSneakers ZHZNVX Polyurethane White Comfort Round Toe Gold Heel Black Flat White Summer PU Women's vp(3, Flat White Comfort Heel Women's Summer Black Polyurethane Round Gold White Toe ZHZNVX Sneakers PU 0); frustum.top.B Heel White Toe PU Round Sneakers Women's Comfort Summer ZHZNVX Gold Polyurethane White Flat Black = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Heel Black Flat Round Toe Summer Gold Polyurethane Women's White Comfort White Sneakers ZHZNVX PU frustum.top.D = -vp(Purple Reebok Shoes White Lilac Trainflex Fitness Shadow Women’s Lilac Lucid Lite XIOXSw1, 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 PU White ZHZNVX White Black Toe Polyurethane Flat Women's Round Gold Comfort Sneakers .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Heel Polyurethane Comfort White Toe Gold Black Flat Round ZHZNVX Women's PU Summer White Sneakers , 2) +Flat Polyurethane Heel White Round ZHZNVX Toe Comfort Black White Summer Gold PU Sneakers Women's vp(3, 2); frustum.right.D = -vp(Cat Eyes Comfort Pattern Women's Cat Casual IDEA 2 Shoes Running Cute HUGS Sneakers xZqPwBOn60, 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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