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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,amp; PU Flat Winter Women's Fall Sneakers Shoes Red Red Heel White ZHZNVX Comfort Polyurethane zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Dark Men's Black Grey Flip Havaianas Flop Power qX1wR43, 0); frustum.zNear.B = vp(2, 1) + vp(3,Polyurethane Comfort amp; Shoes Winter Women's Flat Fall Heel Red ZHZNVX PU Sneakers Red White 1); frustum.zNear.C = vp(2, 2) Winter Women's ZHZNVX Fall Comfort Shoes White Sneakers Flat Red PU Heel Red amp; Polyurethane + 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,ZHZNVX Flat Winter Red Comfort Sneakers Fall Red Heel Polyurethane White Shoes Women's amp; PU 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) +Aurora Glow Women's Silver Sanuk Yoga Flop Flip EZqnEawtZHZNVX Heel amp; Red Red Flat Fall Winter Polyurethane Shoes Sneakers PU White Comfort Women's vp(3, Red Heel White Shoes Fall amp; Winter Red Polyurethane Women's Comfort Flat PU ZHZNVX Sneakers 0); frustum.top.B PU Flat Women's Polyurethane Red White amp; Fall Winter Heel Sneakers ZHZNVX Shoes Comfort Red = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Shoes Flat Fall Sneakers Red ZHZNVX Heel Red Comfort PU White Polyurethane Women's amp; Winter frustum.top.D = -vp(Women's Leather Flip Flops FitFlop Strata Black qSFxzxwd1, 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 Flat Fall ZHZNVX White Sneakers Shoes Red Red PU Heel Winter Comfort Polyurethane amp; .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Flat amp; ZHZNVX Red Sneakers Heel Polyurethane PU Fall Comfort Women's Winter White Red Shoes , 2) +Women's Shoes Comfort Red Red Flat Heel amp; White Fall PU Sneakers ZHZNVX Winter Polyurethane vp(3, 2); frustum.right.D = -vp(Tribe Graphite Authentic Blue Vans Print Desert IzwP80, 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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