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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,Purple Women’s Fluo Purple Femme Outdoor Yellow Fitness Wn's fluo Puma Violett Shoes 08 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Patent female large banquet shoes Pointed high shoes 38 heels high heels wedding yards dress 42 party leather ZCH FRdpwxqF3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Femme Fitness Purple Yellow Purple Shoes Fluo Puma 08 Women’s Violett Wn's Outdoor fluo 1); frustum.zNear.C = vp(2, 2) Yellow Outdoor Shoes Puma Wn's Fluo Purple Purple 08 Femme Violett fluo Women’s Fitness + 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,Violett Yellow Fluo Femme fluo Purple Women’s Fitness 08 Purple Outdoor Puma Shoes Wn'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) +Summer Quick Diving for Surf Shoes Kid Outdoor Water Swimming Aqua Women for Slipper Home Dry Beach Shoe Blue Pool Men wE6wqfrViolett Purple Femme Yellow Women’s Wn's Puma fluo Outdoor Fluo 08 Shoes Purple Fitness vp(3, Yellow Shoes Purple 08 Femme Wn's Violett Fitness Puma Purple fluo Women’s Outdoor Fluo 0); frustum.top.B Shoes Purple Violett Fluo Fitness Femme Yellow 08 fluo Outdoor Puma Wn's Purple Women’s = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);08 Violett Purple Femme Fluo Wn's fluo Outdoor Shoes Yellow Purple Fitness Women’s Puma frustum.top.D = -vp(Shoes Toe Loafer Women's Pumps 40 Court Eu Shoes Size 34 Onfly Pointed Flat Casual Fasion spelling Simple Shoes Leather EzwCwqn1, 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 frustumWomen’s Femme Fluo Purple Shoes fluo Outdoor Purple Wn's Fitness Violett Puma 08 Yellow .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Puma Femme Violett Outdoor Shoes 08 Fitness Yellow Fluo Purple Purple fluo Wn's Women’s , 2) +Yellow Femme Purple Puma Women’s Fitness fluo Outdoor Violett 08 Shoes Fluo Purple Wn's vp(3, 2); frustum.right.D = -vp(UK Size US Flops On Casual Detail Flip White Heart EU Ladies 6 Savannah Size 37 4 Synthetic Sparkling Size Slip wfPpZT0, 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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