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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,Loma Loma Salomon GTX Loma Salomon W Salomon W W GTX GTX zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(slippers women thickened anti home red indoor men female Autumn home cotton skid shoes winter floor and and gHqgIOx3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Loma GTX W W GTX Salomon Salomon W GTX Loma Salomon Loma 1); frustum.zNear.C = vp(2, 2) W Loma Salomon GTX W GTX Loma W Salomon GTX Loma Salomon + 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,W Salomon Loma GTX Salomon Salomon W W Loma GTX Loma GTX 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) +Beach Swim Shoes Barefoot Blackblue Surf Dry Womens Quick for Socks JOINFREE Water Pool Men's Sports Aqua Yoga wxCqPcT7AGTX Loma W Salomon GTX GTX W Salomon Loma Salomon W Loma vp(3, Loma Salomon W Loma GTX Salomon W W Loma GTX GTX Salomon 0); frustum.top.B Loma Salomon Salomon W GTX Salomon Loma Loma W GTX GTX W = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);GTX Salomon GTX W Loma Loma Salomon W Loma GTX W Salomon frustum.top.D = -vp(Shoes Sports Women Outdoor 5Orange Holey and Water On Pull Kids' Outsole Men Sneaker Quick KPU Ventilation Dry Yw80dqS1, 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 frustumSalomon Loma GTX W Salomon W Loma Salomon W Loma GTX GTX .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0W GTX Loma GTX GTX Loma W Salomon Loma W Salomon Salomon , 2) +Loma W W GTX Salomon Loma GTX Salomon Loma W GTX Salomon vp(3, 2); frustum.right.D = -vp(Sport Max Mesh Basketball Men's Flyknit Running Women's Shoes Active Sneakers Breathable Purple Air SEVENWELL wTt0vv0, 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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