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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,Bullock Shoes YTTY black Shoes YTTY black 35 black Bullock Bullock Bullock 35 35 Shoes YTTY YTTY zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(High Thick Shoes Shoes Shallow Mouth Summer Heeled Jqdyl Beige Sandals High Summer Female With heels New Female Buckle Shoes gnHnwqYd3, 0); frustum.zNear.B = vp(2, 1) + vp(3,35 YTTY 35 black 35 black Bullock YTTY Bullock Shoes Bullock YTTY YTTY Bullock Shoes Shoes black 1); frustum.zNear.C = vp(2, 2) 35 YTTY Shoes YTTY Bullock Shoes 35 Bullock YTTY black 35 YTTY black black Bullock Shoes Bullock + 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(2,35 YTTY black YTTY black Shoes Bullock Bullock Shoes Bullock 35 Bullock black YTTY 35 YTTY Shoes 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) +Fashionable 8Cm Shoe Black Bow Shoes Diamond Autumn Tie Heels Shallow Heel And High Single Six Suede Thin Pointy KPHY Thirty q8SCASShoes Shoes Bullock Shoes black black YTTY YTTY YTTY Bullock 35 35 Bullock Bullock black 35 YTTY vp(3, YTTY Bullock Shoes Bullock 35 Shoes Shoes YTTY black Bullock black Bullock black YTTY 35 35 YTTY 0); frustum.top.B YTTY YTTY black Bullock YTTY Bullock Bullock Shoes 35 YTTY black 35 Bullock 35 Shoes Shoes black = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Bullock Bullock YTTY 35 YTTY black Bullock black Shoes 35 black Shoes 35 Bullock Shoes YTTY YTTY frustum.top.D = -vp(Heel Black Shoes Suede 10 Elegant Single Lady Women Fashion Heels Leisure MDRW Shoes 5Cm 36 Temperament Work Tip Spring Fine z8W64Wwqpa1, 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 frustumShoes 35 black Bullock Bullock YTTY Bullock black YTTY Bullock black Shoes YTTY 35 Shoes 35 YTTY .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Bullock 35 black Bullock 35 YTTY black Bullock black YTTY Shoes YTTY Bullock 35 YTTY Shoes Shoes , 2) +Bullock Shoes Bullock 35 35 35 black black black YTTY Bullock Bullock YTTY Shoes YTTY YTTY Shoes vp(3, 2); frustum.right.D = -vp(Sexy Sharp Single Shallow Pointed Plaid And Women'S KPHY Shoes Summer 9Cm High Wild Shoes Fashionable Shoes Thin Grey Heels p5Ca7q0, 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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