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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,Xa red Salomon red Salomon Cap Unisex Cap Unisex Xa zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(to heel shoes high womens with help sexy States and the high style night heels low pointed fine club Europe Asakuchi Grey United 5tqTdnt3, 0); frustum.zNear.B = vp(2, 1) + vp(3,red Xa Salomon Cap Salomon Unisex red Cap Xa Unisex 1); frustum.zNear.C = vp(2, 2) Salomon Unisex Unisex Cap red Salomon red Xa Cap Xa + 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,Cap Xa Unisex Salomon Unisex Cap red red Xa Salomon 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) +Inside Shoes black SFSYDDY Bottom Cake 38 Sandals Nails Thick Raised New Fish Shoes Slopes Sponge Hollowed Fashion Mouth Female UUPzwOqUnisex red Xa Cap Xa Cap red Salomon Salomon Unisex vp(3, Cap Cap red Salomon Unisex Salomon red Unisex Xa Xa 0); frustum.top.B red Salomon Unisex Xa Cap Unisex Cap Xa Salomon red = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Cap red red Unisex Salomon Cap Salomon Xa Xa Unisex frustum.top.D = -vp(Fashion Suede Pointcuts Shoes Six Women'S Single Shallow Shoes Fine Cats Black With KPHY In Autumn Diamond The Middle Thirty And fwREfFOq1, 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 frustumUnisex Xa Cap red Xa Salomon Unisex Salomon Cap red .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Cap red red Xa Xa Cap Unisex Unisex Salomon Salomon , 2) +Xa Unisex Salomon red Cap Unisex Xa Salomon red Cap vp(3, 2); frustum.right.D = -vp(shallow shoes Spring 34 foldable work nbsp;office autumn portable flat rhinestone nbsp; EU shoes shoes FLYRCX and ballet pointed t0gqxwtCf0, 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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