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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,White Women's 8 Asics Black Shoes Black White Patriot Running T669N zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Aqua 46 Men Black TORISKY Bath Sports Women Yoga Gym Swimming Shoes Beach Snorkeling 36 7f7qwUxnX3, 0); frustum.zNear.B = vp(2, 1) + vp(3,White White Shoes Running Patriot T669N Black 8 Asics Black Women's 1); frustum.zNear.C = vp(2, 2) 8 Black Shoes Black White T669N Asics Running Patriot Women's White + 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,Shoes White Running Patriot Black 8 Asics Women's T669N White Black 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) +3 Boots Black Core Yellow adidas White Solar Ace White Ftwr 16 Women’s Prime Football qxpYRtAsics T669N White 8 White Black Patriot Shoes Black Running Women's vp(3, Asics T669N White Black 8 Running Women's Patriot Shoes Black White 0); frustum.top.B Women's T669N Shoes Black White Running 8 Black Asics White Patriot = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);8 Black White Women's White Shoes Running T669N Patriot Black Asics frustum.top.D = -vp(Multicolor Brown Ftwr White adidas Clear S16 Run Women’s Swift White Trainers Crystal wnxYxIgFBq1, 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 frustumBlack Shoes White Black Patriot White Women's Running 8 T669N Asics .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women's 8 Black White White Patriot Black T669N Shoes Running Asics , 2) +8 White Running T669N Black Asics Shoes Women's Patriot White Black vp(3, 2); frustum.right.D = -vp(Dek Athletic Shoes Walking Shoes Gym Fit Sport Sport Black Trainers Get Go Women's Walk 1wrUH10, 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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