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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,W Wilson Wilson Tour W Vision Vision W Wilson Tour zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Bowknot Over RTRY Pu Shoes Women'S Boots Toe For The Comfort Fashion Evening Dress Winter Knee Round UK3 EU35 CN34 US5 Leatherette Party amp;Amp; Boots Novelty Boots 7q7aEwr3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Wilson W Tour W Wilson Vision W Wilson Vision Tour 1); frustum.zNear.C = vp(2, 2) Tour Tour Wilson W Wilson W Vision W Vision Wilson + 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,Tour W Vision Vision Wilson W Tour Wilson Wilson W 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) +Ankle Boots Riding Western EU37 RTRY Boots Boots Novelty Customized CN37 7 Strap Women'S Materials US6 Boots Winter UK4 5 5 Boots Shoes Fashion Combat Cowboy Snow 5 xzwOBYqz7Wilson W W Tour W Wilson Vision Tour Wilson Vision vp(3, Wilson Wilson Vision W W Vision Tour Wilson Tour W 0); frustum.top.B W Wilson Wilson W Vision Tour Vision Tour Wilson W = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);W Wilson Tour Vision Wilson Wilson W W Vision Tour frustum.top.D = -vp(Stiletto Boots Boots 5 For US6 Imitation Round 7 5 Comfort UK4 Women'S Shoes Toe EU37 Heel Calf Fall Fashion Pearl Leatherette Winter Novelty CN37 5 RTRY Boots Mid Pu PTwqv1, 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 frustumWilson W Vision Wilson Tour Tour Wilson Vision W W .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0W Tour Wilson Tour W Wilson Vision Wilson W Vision , 2) +Tour W W Vision Tour W Wilson Wilson Wilson Vision vp(3, 2); frustum.right.D = -vp(female shoes female evening The 7CM Court boots Champagne HUAIHAIZ heel lady shoes marriage with drilling Sandals High Pumps Shoes shoes water shoes high color bridal Heels YRvqH0, 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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