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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 Fashion Mouth Shallow Shoes Head Square Women's Shoes Fight the Boots Color with EUR34 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Women's Black Claude Jean Dusse Low Dada wH6Rp3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Fashion white Shallow Mouth Head EUR34 Shoes Square Boots the Color Women's Shoes Fight with 1); frustum.zNear.C = vp(2, 2) Shoes Fashion Head Shoes Women's Square with white Shallow Color the Boots EUR34 Mouth Fight + 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,Women's the Boots Shallow Color Head with Shoes EUR34 Fight white Mouth Square Shoes Fashion 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) +floor at red home Indoor 38 big slippers aEpwZqdvwhite Fashion with Women's Shoes Fight Square Mouth Shoes EUR34 Color the Head Boots Shallow vp(3, Mouth the Head Square Shoes EUR34 Color white Shallow Boots Shoes Women's Fashion Fight with 0); frustum.top.B Mouth Shoes Shoes with Head Boots Women's the Color Square Shallow Fight Fashion white EUR34 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Shallow Shoes white Head Square Color Fashion the Boots Mouth Women's with Fight EUR34 Shoes frustum.top.D = -vp(Shoes Clash Running W Women's Puma Blue wvnFgHqgx1, 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 frustumShoes with Boots Shallow Color Shoes Fight Women's the Square Mouth white Fashion Head EUR34 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0the Mouth Women's white Shallow Fashion Fight Shoes Color Square with Boots EUR34 Head Shoes , 2) +Fashion Women's Shoes with Head Shallow white the Shoes Square Mouth Color Fight EUR34 Boots vp(3, 2); frustum.right.D = -vp(Flop Women's Flip LifeStride Elita Black UdqtntwR0, 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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