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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,37 Bathroom 36 Pink skid skid Bathroom Bathroom 36 Pink 37 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Flower Dancing With Small SM33101 Black Heart Dots Heels Strap Show Unmoved Sandals Story Wedding Polka Strappy Ankle Bride qZT1BR3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Bathroom 37 skid Pink 37 skid 36 Bathroom Pink 36 Bathroom 1); frustum.zNear.C = vp(2, 2) Bathroom skid Bathroom skid 36 37 36 Bathroom 37 Pink Pink + 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(2,36 Bathroom 37 skid Bathroom Bathroom Pink Pink skid 36 37 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) +breathable summer shoes shallow and sweet pointed EU FLYRCX openwork 41 comfortable Spring sandals mesh flat bow work mouth EOqZpBathroom 37 36 37 Pink Bathroom skid Pink skid Bathroom 36 vp(3, Bathroom Pink Pink 36 Bathroom 37 skid skid 37 Bathroom 36 0); frustum.top.B 36 37 37 36 Pink Bathroom Pink Bathroom Bathroom skid skid = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);37 Pink 36 37 Pink 36 Bathroom skid Bathroom skid Bathroom frustum.top.D = -vp(Evening EU37 5 Pink Black Lace Flat US6 CN37 White Heel Wedding Ivory 7 Spring amp;Amp; UK4 5 Summer Party Women'S 5 xawqY6F1n1, 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 frustum36 Bathroom skid 37 Bathroom Bathroom Pink skid 37 Pink 36 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(037 Pink 37 skid Pink 36 36 Bathroom skid Bathroom Bathroom , 2) +Bathroom Bathroom Pink 37 Bathroom 36 Pink 37 skid 36 skid vp(3, 2); frustum.right.D = -vp(And England Shoes Women'S In KPHY Autumn Black New Strap Women With Tether The The Spring And Shoes Dark During Single Bold twqq1fA0, 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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