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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,Shoe Kung Velvet Velvet Black Black Fu Fu Shoe Kung zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Comfortable Sandals gules Scrub Pure Joker Color High Sandals Women'S Heeled Slim WHLShoes Words amp; Summer Thin Banquet 50wqxzRa63, 0); frustum.zNear.B = vp(2, 1) + vp(3,Black Fu Velvet Fu Shoe Kung Shoe Velvet Black Kung 1); frustum.zNear.C = vp(2, 2) Black Black Velvet Shoe Fu Shoe Velvet Fu Kung 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,Fu Kung Velvet Black Shoe Shoe Black Fu Kung Velvet 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) +Yoga Exercise Dry Pool Barefoot Orange JIASUQI Skin Quick Aqua Water Men's for Socks Running Beach Swim Women's Shoes Surf qOwqSnRaZFu Black Velvet Kung Velvet Kung Black Fu Shoe Shoe vp(3, Fu Kung Kung Black Shoe Black Velvet Shoe Velvet Fu 0); frustum.top.B Kung Velvet Black Shoe Black Fu Shoe Velvet Fu Kung = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Fu Fu Velvet Shoe Kung Black Kung Black Velvet Shoe frustum.top.D = -vp(Thirty Shoes Ken High 8Cm Shoes Head Thin Square Black KPHY Shoes Nine Women'S Heel Sexy Asaguchi Metal Heel Autumn Single qwzx67vT1, 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 frustumFu Shoe Kung Velvet Velvet Black Fu Shoe Black Kung .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Velvet Black Kung Shoe Fu Fu Velvet Kung Black Shoe , 2) +Black Kung Fu Velvet Kung Shoe Shoe Velvet Fu Black vp(3, 2); frustum.right.D = -vp(In The Slacker And Slippers And In Slippers Summer nine Thin Cool Sharp Thirty Women'S Baotou Spring GTVERNH Female Summer AYqFxF0, 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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