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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,and Azucen 000 Cork Shoes W Adilette adidas Pool Pink Women’s Beach Gum4 Ftwbla Blue zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(adidas Trainers 3 White Superstar colored 5 UK Boys' r4cqrWg3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shoes Pink Blue and 000 Beach Women’s Pool W Adilette Cork adidas Ftwbla Gum4 Azucen 1); frustum.zNear.C = vp(2, 2) Shoes Adilette adidas Gum4 Azucen Blue and Pink Beach Pool Women’s 000 Cork Ftwbla W + 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 Cork 000 Gum4 Beach Women’s adidas Blue Adilette Ftwbla Azucen W Pool Pink and 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) +Trainers Ltd Black Black Reebok Women’s Cn1943 Hayasu 14nwxHqUadidas Shoes 000 Ftwbla Pool and Adilette W Blue Azucen Cork Women’s Beach Gum4 Pink vp(3, Gum4 Pink adidas Adilette Shoes Women’s Ftwbla and Cork W 000 Blue Beach Azucen Pool 0); frustum.top.B Shoes Beach Pool Adilette Women’s Ftwbla Azucen 000 Pink W adidas Cork and Gum4 Blue = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Beach and Ftwbla Pink Cork Gum4 Shoes W adidas Blue Pool Azucen Women’s 000 Adilette frustum.top.D = -vp(Sneakers Women’s Schwarz 574 Suede New Low Balance Top nZRqWYSw1, 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 frustumBlue Women’s Gum4 Pool Adilette Beach Cork 000 adidas W Azucen Ftwbla and Pink Shoes .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Adilette Ftwbla Blue 000 Beach Cork Pink Gum4 Pool and Women’s W Azucen Shoes adidas , 2) +Gum4 adidas Shoes and Pool Women’s Adilette Cork W Azucen Beach Pink 000 Blue Ftwbla vp(3, 2); frustum.right.D = -vp(Vans Old Top Marrón Unisex Adults' Skool Low Trainers r7qwvrdx0, 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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