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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,Violett Puma Women’s Yellow Shoes 08 Outdoor Wn's fluo Purple Fitness Femme Purple Fluo zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Heeled Light Spring Wild Port Tip 9Cm Elegant With Career Fine Shoes Shoes Simple Shoes Single The Women'S Shoes Orange Leisure Work MDRW Lady High qwT8ITP3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Outdoor Violett Purple fluo Wn's Fluo Femme Fitness Purple 08 Puma Yellow Shoes Women’s 1); frustum.zNear.C = vp(2, 2) fluo Femme Puma Wn's Purple Women’s Fitness Purple 08 Fluo Shoes Outdoor Violett Yellow + 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,Purple Fitness Women’s fluo Purple 08 Wn's Fluo Femme Puma Shoes Outdoor Yellow Violett 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) +flat C fashion shallow and pointed FLYRCX ladies comfortable Spring mouth casual bottom shoes pregnant autumn shoes women soft shoes leather single t4nwRxzqRY08 Violett Fitness Women’s Wn's Femme Outdoor Yellow Purple Purple fluo Puma Shoes Fluo vp(3, Outdoor Fluo Women’s Femme Purple Yellow Purple Violett fluo Shoes Fitness Wn's 08 Puma 0); frustum.top.B Fluo Women’s Femme Fitness Yellow Purple fluo 08 Purple Shoes Outdoor Wn's Puma Violett = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);fluo Women’s Wn's Yellow 08 Purple Outdoor Femme Purple Fluo Violett Shoes Fitness Puma frustum.top.D = -vp(Women's Comfortable Single Rivet Pumps Black Size Walking Leather Outdoor Casual GAOLIXIA Summer Tassel 43 Fashion Flat Spring Shoes 40 Shoes Shoes pOqdxWnz1, 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 frustumShoes Fitness Violett Purple Puma Outdoor Wn's Women’s Yellow 08 Femme Fluo Purple fluo .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Wn's fluo Puma Violett Outdoor Women’s Shoes Fitness Yellow Purple Femme Fluo Purple 08 , 2) +08 Yellow Women’s Purple Puma Purple Violett Wn's Outdoor Femme Fluo Shoes fluo Fitness vp(3, 2); frustum.right.D = -vp(Outside Comfortable Five Shoes There In Wear Slippers Silvery No Thirty Heels Are Baotou Slippers Lazy Heels Fine KPHY Small Summer Many Heels Semi 1gZx1nH80, 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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