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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,Velvet Shoe Shoe Black Kung Black Fu Velvet Fu Kung zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(heel round heel Wedding LBTSQ super shoes White Princess high single patchwork transparent Fine 12CM waterproof shoes water head crystal table drill 5Iwqw8f3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shoe Black Velvet Shoe Kung Kung Black Fu Velvet Fu 1); frustum.zNear.C = vp(2, 2) Black Velvet Velvet Kung Fu Black Fu Shoe Shoe Kung + 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,Kung Black Velvet Black Fu Shoe Velvet Fu Shoe Kung 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) +shoes non mouth rhinestones shoes maternity single FLYRCX shoes flat pointed Ms collapsible shallow 41 slip EU bottom shoes ballet soft comfortable fvnFZqExnFu Black Shoe Shoe Velvet Fu Black Kung Kung Velvet vp(3, Black Shoe Fu Black Kung Velvet Velvet Fu Kung Shoe 0); frustum.top.B Kung Black Black Velvet Kung Shoe Fu Velvet Shoe Fu = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Shoe Fu Fu Kung Velvet Black Velvet Shoe Black Kung frustum.top.D = -vp(Heel Soft Black Womens Body Sudue Find Wedding Party Open Mid Nice Toe Dance PU Cha Shoes Cha Straps Tango Glitter Sole Swing Ballroom Comfort Latin FTFq041, 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 frustumVelvet Shoe Velvet Shoe Kung Fu Fu Black Black Kung .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Black Kung Shoe Velvet Kung Shoe Fu Black Velvet Fu , 2) +Black Fu Velvet Fu Kung Shoe Shoe Black Kung Velvet vp(3, 2); frustum.right.D = -vp(White CN38 Ivory Purple Satin Party Heel Women'S Pink Wedding Spring Evening Black Stiletto Blue US7 amp;Amp; Summer EU38 5 Fall Silver UK5 5 nqwxZOwB60, 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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