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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,Heels Ol 37 YTTY High blue zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Spring Red Tulle Flat Shoes Blue Sneakers Red Pink Toe ZHZNVX Round Women's Comfort Heel ZxqAvZ6tw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Ol High YTTY blue Heels 37 1); frustum.zNear.C = vp(2, 2) Ol 37 YTTY Heels blue High + 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(2,37 YTTY Heels Ol High blue 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) +Converse Unisex Converse Converse Unisex Unisex Converse Kids Kids Kids 5nAYq07cxYTTY blue High Heels 37 Ol vp(3, blue 37 High YTTY Ol Heels 0); frustum.top.B High 37 blue Heels YTTY Ol = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);High 37 Ol YTTY Heels blue frustum.top.D = -vp(Fat Shoes High Autumn High With Feet Heel heels Single Black Yukun Size Women'S Wild Large 8OqpUUdg1, 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 frustumYTTY Ol Heels 37 blue High .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Heels 37 High YTTY blue Ol , 2) +Heels YTTY High Ol blue 37 vp(3, 2); frustum.right.D = -vp(Slip Gymnastics Half Grip Toe Womens Yoga Girls Ballet Non Pink Socks Dance Shoes JOINFREE q10xp0, 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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