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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,Women's Lunar Pure Off Shoe Nike US White Skyelux Women Running Platinum 5 9 White zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Elastic GLTER Pump Sandals New Size Summer Embossed Wedge Shoes Pointed WOMEN Large Slingback 40 Toe 43 Black 7q6wz7rtS3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Skyelux White 9 White Off Women Lunar US Running Nike Shoe 5 Women's Pure Platinum 1); frustum.zNear.C = vp(2, 2) US Women Nike 5 White Lunar Women's Off Running Skyelux Shoe Platinum 9 White Pure + 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 Off Skyelux Shoe White US Running Pure Lunar 9 White Women's Nike 5 Platinum 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) +Heels White Yellow Heel amp; Polyurethane Pink Women's Block Summer ZHZNVX Shoes Yellow Spring PU Comfort PRvP8nxUS Shoe White Women's Pure Nike Lunar Running Off Skyelux 5 White Women 9 Platinum vp(3, Women's Nike Shoe Pure 9 Off Running White Platinum US Women White 5 Skyelux Lunar 0); frustum.top.B Running 9 Skyelux Shoe Pure US Nike Platinum White Women 5 White Lunar Off Women's = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Running 9 White Women US Shoe Lunar Women's White Nike Pure Platinum Off 5 Skyelux frustum.top.D = -vp(ZHZNVX Pink Nappa Almond Heel Heels amp; Leather Summer Spring Black Women's Shoes Yellow Comfort Stiletto 7rZq7B1, 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 frustumLunar White Running White Off 5 Pure Women's Platinum Women Nike Skyelux US Shoe 9 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women's Pure White Women Shoe Skyelux US Running Lunar 9 Nike 5 Platinum White Off , 2) +Pure Off White Running Women Women's Shoe Skyelux Lunar White 9 Nike Platinum US 5 vp(3, 2); frustum.right.D = -vp(And Shoes Zipper Fine Thirty European Suede GTVERNH Naked Side Heel Boots High six American Heel New Marriage Yxn5qxBw1F0, 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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