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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,Snake YTTY YTTY Shoes Snake Snake 37 YTTY Shoes Shoes black black 37 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Square Heel Winter Ankle Khaki Casual Fashion Chunky Shoes Nubuck ZHZNVX Dress HSXZ Women's Booties Boots leather Spring for Black Boots Toe Khaki Boots nxqPwg7ZRw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,black YTTY Snake Snake Shoes Snake YTTY Shoes 37 black YTTY 37 Shoes 1); frustum.zNear.C = vp(2, 2) YTTY YTTY Snake 37 Snake black Shoes Snake black Shoes Shoes 37 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,YTTY Shoes 37 Snake Snake YTTY Shoes black 37 Snake Shoes black YTTY 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) +Toe Fall Null Fashion Comfort Boots HSXZ Ankle leather Booties ZHZNVX Heel Boots Black Casual Boots for Nubuck Block Round Shoes Winter PU Black Women's 4A7qw0axShoes Shoes Shoes YTTY YTTY 37 black YTTY 37 Snake Snake Snake black vp(3, Shoes black Shoes Snake 37 YTTY black Shoes Snake Snake 37 YTTY YTTY 0); frustum.top.B YTTY YTTY 37 Snake 37 Shoes Shoes Shoes Snake YTTY black Snake black = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);37 Shoes Snake Shoes Snake Shoes black YTTY black YTTY YTTY Snake 37 frustum.top.D = -vp(Winter Boots Nappa Lining For Fashion 7 Beige Boots UK4 Leather CN37 5 Fall EU37 Brown Ankle RTRY Women'S 5 Fluff Booties 5 Boots Casual US6 Shoes 6Ewx0qEfnX1, 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 Snake 37 37 YTTY Snake YTTY Shoes black Snake black Shoes Shoes .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(037 YTTY Shoes YTTY YTTY 37 Shoes black Shoes Snake black Snake Snake , 2) +37 Snake YTTY Snake Shoes Shoes black Shoes YTTY YTTY black 37 Snake vp(3, 2); frustum.right.D = -vp(All Hair Single Famous High 9Cm Summer Shoe Buckle Cat Thin Shoes Heel Wind And Women'S Sexy Shoes Heel Jokes Beige Heel Kinds One Of Pointed Word KPHY 5qSwxBPt0, 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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