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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,Summer Dance Fitness Ladies Sole Sneakers VECJUNIA Soft Rose Shoes Modern Red zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(flops female XZ LIUXINDA British slippers bottom cold slippers flip fashion Beige heel slippers High drill water slippers thick qUa1wq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shoes Sole Summer Dance Sneakers Soft Modern Fitness VECJUNIA Red Rose Ladies 1); frustum.zNear.C = vp(2, 2) Rose Fitness Summer Soft Modern Shoes Sneakers VECJUNIA Ladies Dance Red Sole + 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,Shoes Sole Rose Red VECJUNIA Modern Sneakers Soft Summer Fitness Ladies Dance 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) +Grip Lacyie Toe Yoga Skid For Toe Dance Anti Non Women Fitness Socks Five Half 37 38 Slip Pilates Shoes Socks Yoga Pink Cotton Soles qFrvtqp0Red Soft VECJUNIA Modern Sole Sneakers Rose Shoes Fitness Ladies Summer Dance vp(3, Rose Fitness Soft Red Summer Ladies VECJUNIA Sneakers Sole Modern Shoes Dance 0); frustum.top.B Fitness Shoes VECJUNIA Rose Modern Ladies Summer Dance Soft Sole Sneakers Red = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Fitness Shoes Dance Sole Summer Ladies Modern Soft VECJUNIA Rose Sneakers Red frustum.top.D = -vp(work fashion single shoes soft shoes Fashion pregnant FLYRCX bottom women spring shoes autumn Black comfortable and casual flat shoes HOxPwq81, 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 frustumRose Red Fitness VECJUNIA Shoes Sneakers Modern Soft Ladies Dance Summer Sole .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Dance VECJUNIA Ladies Rose Red Sneakers Modern Sole Soft Summer Shoes Fitness , 2) +Fitness Sole Summer Rose Red VECJUNIA Soft Dance Shoes Sneakers Ladies Modern vp(3, 2); frustum.right.D = -vp(Skin Men RIBIKA Diving Black Dry Boating Yoga Socks Swimming Lake Shoes Aqua Womens Walking Barefoot for Beach Quick Surf Shoes Park qFtFpx70, 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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