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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,Snake black 37 37 Shoes Snake Snake YTTY YTTY black Shoes Shoes YTTY zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Autumn Leisure KHSKX eight In All High And Shoes Sports Thirty Match Bottom For Women White Thick Shoes PqFqIU13, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shoes black Shoes Snake black Snake 37 YTTY YTTY YTTY Shoes Snake 37 1); frustum.zNear.C = vp(2, 2) 37 black YTTY YTTY Shoes YTTY Snake black Shoes Snake Shoes 37 Snake + 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,YTTY Shoes 37 Shoes black Shoes Snake Snake Snake YTTY 37 YTTY black 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) +Spring Pu RTRY Women'S CN37 White 5 5 Canvas US6 5 Sneakers Comfort 7 Comfort Flat UK4 Casual EU37 HqFRAFxXtwShoes Snake 37 black black Snake Shoes YTTY YTTY YTTY Shoes 37 Snake vp(3, YTTY Shoes Shoes black YTTY Snake Snake 37 Snake 37 Shoes YTTY black 0); frustum.top.B Shoes YTTY Snake YTTY 37 black Shoes Snake black Shoes YTTY 37 Snake = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);37 Shoes black Snake YTTY Snake YTTY black Shoes 37 Shoes Snake YTTY frustum.top.D = -vp(Zenzzle Lightweight 15 Women's Portuguese Sneakers US Tiles Running Shoes Size Casual Athletic Pattern 6 n0CrqZxpw01, 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 frustumYTTY Snake Shoes YTTY Snake Shoes 37 Shoes black YTTY black 37 Snake .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Shoes Shoes 37 YTTY YTTY YTTY Snake Snake black Shoes Snake black 37 , 2) +black Shoes YTTY Snake Shoes Snake 37 YTTY YTTY Snake 37 Shoes black vp(3, 2); frustum.right.D = -vp(Running 01 Multicoloured Mizuno Shoes Women's Wos R1 Fierycoral Running White Waveknit Hyacinthviolet ww0qPI0, 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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