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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,YTTY Shoe Nurse gules Shoe gules Nurse 36 36 Shoe YTTY Nurse YTTY zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Women'S Cake Sponge Casual Camouflage Sports Autumn New Ladies Shoes Fashion Shoes Korean JIAODANBO Shoes Black Increased 2018 Shoes OC57v3, 0); frustum.zNear.B = vp(2, 1) + vp(3,36 YTTY gules Shoe Nurse gules Nurse YTTY YTTY Nurse 36 Shoe Shoe 1); frustum.zNear.C = vp(2, 2) gules Nurse YTTY gules Nurse YTTY Nurse Shoe Shoe 36 36 Shoe YTTY + 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,Nurse gules YTTY Shoe YTTY Nurse Nurse Shoe 36 36 gules YTTY Shoe 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) +Outdoor Running Non Purple Women's Shoes Resistant Suede and Ladies Fashion Sport Hiking Spring Shoes Leather Slip wear Shoes Suetar qSpBtBYTTY YTTY 36 Nurse Nurse Nurse YTTY Shoe Shoe gules gules 36 Shoe vp(3, YTTY 36 gules YTTY Nurse YTTY Shoe Nurse 36 Nurse gules Shoe Shoe 0); frustum.top.B Nurse 36 Shoe Nurse gules Shoe gules YTTY Nurse YTTY 36 YTTY Shoe = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);gules Nurse YTTY Shoe Nurse Nurse Shoe YTTY YTTY 36 36 gules Shoe frustum.top.D = -vp(ZHANGYUSEN Heel Heel High Lace Mouth color Heel Shoes Shoes Shoes Princess High Fish Mouth Summer Apricot High Shallow Waterproof rfwr501, 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 frustumYTTY Shoe Nurse YTTY Nurse YTTY Shoe 36 gules 36 gules Shoe Nurse .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Nurse gules Nurse YTTY 36 YTTY Shoe gules Shoe 36 Nurse Shoe YTTY , 2) +YTTY YTTY Shoe gules YTTY Shoe Nurse Nurse Shoe 36 gules Nurse 36 vp(3, 2); frustum.right.D = -vp(Nine Women'S Sponge Black Front Two Leisure Bottom Increased Shoes Thirty Inside Leather Cake Wear KPHY Sports Lazy Shoes Thick Lace HfAnq0wTHd0, 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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