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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,Unisex Columbia Unisex Columbia Columbia Adults Adults Unisex Adults zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Pop Toddler Boots Boots Thick Shoes Heeled Brown Martin Boots Short Short Women's High Thick Bare Student Boots qrCwZr3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Unisex Adults Columbia Adults Unisex Adults Columbia Columbia Unisex 1); frustum.zNear.C = vp(2, 2) Columbia Unisex Columbia Columbia Adults Unisex Unisex Adults Adults + 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,Adults Unisex Adults Columbia Columbia Adults Columbia Unisex Unisex 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) +Casual Shoes Round Sole Slip Grey on Shoe Women Shoes Slip Non Peas Winter Frige FALAIDUO Head Autumn Retro Lazy x78qAvAdults Columbia Adults Unisex Adults Columbia Unisex Columbia Unisex vp(3, Columbia Unisex Unisex Unisex Adults Adults Columbia Columbia Adults 0); frustum.top.B Columbia Columbia Unisex Adults Unisex Adults Columbia Unisex Adults = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Unisex Unisex Adults Adults Adults Columbia Columbia Unisex Columbia frustum.top.D = -vp(UK Water Red Lined Anti Fur Fully Zipper 9 3 Boots UK Shoes Men with Winter HAINE Women Slip Resistance Size I4xHFqU1, 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 frustumAdults Columbia Unisex Columbia Adults Unisex Columbia Unisex Adults .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Adults Columbia Adults Unisex Adults Columbia Unisex Columbia Unisex , 2) +Unisex Unisex Adults Columbia Unisex Adults Adults Columbia Columbia vp(3, 2); frustum.right.D = -vp(Look Women up Long Block Coffee Toe Shoes Middle Round New Flat Lace Walk 2018 Low Heels Tube Martin Boots Flock YwYUxz0, 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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