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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,Polyurethane Heel PU Women's Red Red White Fall amp; Comfort ZHZNVX Sneakers Shoes Winter Flat zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Gel Women's Black TR Pistachio Fortius Asics Training 2 Shoe Silver gHZwOq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Heel Winter Red PU amp; Fall Polyurethane Women's Sneakers Comfort Flat Red White Shoes ZHZNVX 1); frustum.zNear.C = vp(2, 2) Comfort Shoes Women's ZHZNVX Red Fall Red Heel Polyurethane Sneakers Winter PU amp; Flat White + 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,Comfort Flat PU Heel Red Shoes White ZHZNVX Winter Sneakers amp; Women's Fall Polyurethane Red 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) +boots winter in increase round boots matte flat tube Brown size The tZpHqqZHZNVX Polyurethane Flat amp; Fall Red Comfort Heel White PU Red Shoes Women's Winter Sneakers vp(3, White ZHZNVX Red Winter Women's Sneakers Red Comfort Shoes Fall amp; Heel Polyurethane PU Flat 0); frustum.top.B PU Polyurethane ZHZNVX Comfort Sneakers White Fall Flat Winter Red Red Heel amp; Shoes Women's = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Fall PU Comfort White amp; ZHZNVX Polyurethane Red Sneakers Heel Flat Women's Winter Shoes Red frustum.top.D = -vp(665 Cushioning Balance New Black With Womens Purple Shoes Walking EqRvcHUvpw1, 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 frustumPU Red Polyurethane Sneakers Shoes Flat ZHZNVX Women's Comfort Red Winter amp; White Heel Fall .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Comfort White Women's ZHZNVX Shoes Fall Red PU Polyurethane Winter Sneakers Heel Red Flat amp; , 2) +ZHZNVX Shoes Red PU Red Sneakers Winter Comfort Fall amp; Polyurethane Flat Heel Women's White vp(3, 2); frustum.right.D = -vp(Pink Berry 5 Asics White Shoes Tennis Women’s Gel Pink Game Plum wAxB8q0, 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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