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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,Press Shoes Women’s W Under Armour 2 Black Fitness Ivory 101 Grey White Ua zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Smith Shoes Originals adidas Stan Weiß Men’s Running wAtwxX0v3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Women’s 101 White 2 Shoes Black Grey Ua Press Armour Ivory W Fitness Under 1); frustum.zNear.C = vp(2, 2) 101 Armour Ua Black Fitness Ivory Shoes White W Press Grey Women’s 2 Under + 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,Armour Ivory White Grey 2 W Black Under Shoes Ua Women’s Fitness Press 101 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) +Unisex Old Top Low Trainers Skool Blue Adults' Vans 4qTR4w101 Armour W Fitness Grey Ua Ivory Shoes Under White Press Women’s Black 2 vp(3, 2 Ivory W Black Under Press 101 Grey Women’s Shoes White Fitness Ua Armour 0); frustum.top.B Fitness W Press Grey White Ua Ivory Women’s 2 Black 101 Shoes Armour Under = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Shoes Ivory Grey Black W Ua 2 Armour Fitness Under Press 101 White Women’s frustum.top.D = -vp(25 Table Hbr Men's Red Shirt Nike Black T University p4ntxxOS1, 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 frustum101 W Fitness 2 Press Shoes Armour White Ua Black Under Grey Women’s Ivory .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0101 Fitness W Under 2 Ua Women’s White Press Black Armour Grey Shoes Ivory , 2) +Ua 2 White Under Women’s Armour Press Shoes W Grey 101 Fitness Ivory Black vp(3, 2); frustum.right.D = -vp(4 EU Revolution Blue Shoes Women’s Nike WMNS Running OwqTBx0, 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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