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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,Riding Birgit Boots Black Birgit Riding zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Heelivory Crystal US5 5 RTRY Shoes Summer Wedding Light Spring Pink Stiletto Evening Party Pump Women'S amp;Amp; Purple CN35 5 EU36 Satin Wedding Stretch Ruby Basic UK3 OqRZxfO3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Riding Riding Birgit Black Birgit Boots 1); frustum.zNear.C = vp(2, 2) Birgit Birgit Black Riding Boots Riding + 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,Birgit Riding Black Boots Birgit Riding 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 Dress Leatherette Stiletto CN35 Heels Print Evening Purple US5 Animal 3 Slingback Summer amp;Amp; Heel EU36 RTRY Brown UK3 5 Women'S White3In 5 Party Light Black xFzCqn7nIwBlack Riding Riding Boots Birgit Birgit vp(3, Birgit Black Riding Boots Riding Birgit 0); frustum.top.B Black Birgit Boots Birgit Riding Riding = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Black Birgit Riding Birgit Boots Riding frustum.top.D = -vp(Party White 5 Women'S Flat amp;Amp; Rhinestone EU43 Evening Purple Winter Blue Summer Satin Black Silver Spring Wedding UK9 US11 Ivory CN45 Casual 5 Heel Fall RTRY Pink Hwpq81, 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 frustumRiding Boots Riding Birgit Black Birgit .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Birgit Riding Riding Black Boots Birgit , 2) +Birgit Black Riding Boots Birgit Riding vp(3, 2); frustum.right.D = -vp(Pu US6 UK4 Spring Basic Wedding Evening amp;Amp; Summer amp;Amp; Pu Pump Bucklechunky Microfiber Office CN36 Party Synthetic Women'S Career EU36 Heels Dress Basic Pump 5xRqBw00Y0, 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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