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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,fluo Violett Yellow Purple 08 Women’s Outdoor Femme Shoes Purple Fluo Fitness Puma Wn's zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Gry Running Competition Shoes Champion Schwarz Women’s Alpha Black Lib TqRUn6Yxw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Violett Outdoor Purple 08 Fitness Fluo Puma Shoes Women’s Purple Femme fluo Wn's Yellow 1); frustum.zNear.C = vp(2, 2) Yellow Violett 08 Fitness Puma Purple Femme Women’s Purple Fluo fluo Wn's Outdoor Shoes + 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,Yellow Wn's Femme Violett 08 fluo Purple Puma Shoes Women’s Fitness Fluo Purple Outdoor 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) +12 ttl Crmsn Nike Women’s WMNS Hypr white Blk Viola Vlt Dart Gymnastics qzw1xER4zShoes Fluo Puma Wn's Yellow Femme Fitness Outdoor Violett Purple Purple Women’s fluo 08 vp(3, Purple Violett Yellow Fluo Outdoor Shoes Wn's 08 fluo Fitness Puma Purple Femme Women’s 0); frustum.top.B Puma Femme Women’s Fluo Fitness Wn's Outdoor 08 Yellow fluo Shoes Purple Purple Violett = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Women’s Purple Shoes Femme Fluo Purple Wn's fluo Fitness Puma Violett Yellow 08 Outdoor frustum.top.D = -vp(Women's Pure Trainer Gray X Boost Shoe Performance TR adidas Light 2 Cross 5ETq11, 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 frustumPurple Shoes Puma 08 Fitness Purple Fluo Women’s Outdoor Yellow Violett fluo Femme Wn's .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Femme Fluo Wn's Purple 08 Puma fluo Purple Women’s Yellow Shoes Fitness Outdoor Violett , 2) +Puma Yellow Purple Outdoor Women’s Fluo Femme Fitness Wn's 08 fluo Shoes Purple Violett vp(3, 2); frustum.right.D = -vp(Under Speedform Armour US Running MSV Ptp M Blk Shoe Europa Blue Women's fxBrdwf0, 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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