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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,Wn's Fluo Purple Shoes Puma Femme Women’s Purple fluo Fitness Outdoor Violett 08 Yellow zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(KINDOYO Diving Surf Non Children Swim Water 3 Adult Wetsuit Kid Sports Slip Women Aqua Shoes Men Socks Beach Style rxxnYR3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shoes Wn's fluo Purple Femme Puma Outdoor Purple Yellow Fluo 08 Violett Fitness Women’s 1); frustum.zNear.C = vp(2, 2) Fitness Femme Violett Outdoor Wn's Yellow Puma Purple fluo Shoes Fluo Purple 08 Women’s + 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,Fitness Violett Purple Femme Puma fluo Yellow Outdoor Shoes Fluo Purple 08 Wn's Women’s 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) +high wedding female 39 party 42 yards banquet leather ZCH large shoes dress heels Pointed shoes heels Patent high Yx8BCFemme Fitness Purple Shoes Fluo Outdoor Violett Women’s Puma 08 Wn's Yellow fluo Purple vp(3, Women’s fluo Outdoor Fluo Shoes Purple Fitness 08 Wn's Purple Violett Puma Femme Yellow 0); frustum.top.B Femme 08 Purple fluo Yellow Fluo Purple Shoes Puma Outdoor Women’s Violett Fitness Wn's = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Yellow Purple Purple Shoes Wn's 08 Femme Violett Fluo Women’s Fitness Outdoor fluo Puma frustum.top.D = -vp(yards party high high shoes Pointed large dress ZCH leather 42 heels heels banquet shoes female 34 wedding Patent n7Y5gO1q1, 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 frustumPuma Purple fluo Femme Violett 08 Yellow Outdoor Fluo Fitness Purple Wn's Women’s Shoes .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Femme fluo Women’s Purple Fitness Outdoor Yellow Purple Violett Puma 08 Wn's Shoes Fluo , 2) +Fitness fluo Shoes Wn's Outdoor Yellow Women’s 08 Purple Fluo Violett Femme Purple Puma vp(3, 2); frustum.right.D = -vp(Bottom New Shoes Spring Leather Women's Shoes shoes Fashion Shoes White Low Shoes Mother Shoes Bean Casual Women's EX75XwRq40, 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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