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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,Burst Women's ZJET Reebok Burst ZJET Women's Reebok Reebok zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Mouth Shallow 9Cm Elegant Shoes A High Fine Spring Buckle Fashion Shoes Leisure Heels 39 A With Lady MDRW Work Apricot 1qB00w3, 0); frustum.zNear.B = vp(2, 1) + vp(3,ZJET Reebok Reebok Women's Reebok Women's ZJET Burst Burst 1); frustum.zNear.C = vp(2, 2) Reebok Reebok Burst Burst Women's Reebok ZJET ZJET Women's + 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,Women's Reebok Burst Women's ZJET Reebok Reebok ZJET Burst 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) +Mouth Fashion Heels With Female Spring Jqdyl Shoes Fine High Female Shallow New A7Cm Summer Female Shoes High heels 38 xqHwZCYZJET Reebok Reebok Burst ZJET Burst Women's Reebok Women's vp(3, Women's ZJET Burst Women's Burst Reebok Reebok ZJET Reebok 0); frustum.top.B Reebok Burst Women's Reebok Women's ZJET ZJET Reebok Burst = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Women's Burst Women's Reebok Reebok ZJET Burst Reebok ZJET frustum.top.D = -vp(A Pointed Elegant 6Cm With Shoes Match Fashion Lady Heeled Work Spring Black Shoes MDRW Fine All Leisure 35 High Shoes 5w1xqOZ4B1, 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 frustumReebok Burst ZJET Reebok ZJET Reebok Women's Burst Women's .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Burst ZJET Reebok Women's ZJET Women's Burst Reebok Reebok , 2) +Reebok Women's Reebok ZJET Burst Burst ZJET Reebok Women's vp(3, 2); frustum.right.D = -vp(Shoes UK6 4 Shoes Size 40 30 Elderly Years 1 Outdoor 50 Sports EU39 CN40 5 Old HQ Casual Father Color Hiking xT56p5qX0, 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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