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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,SHOES High 40 Naked Color size Big knot Round FYM Color heel Solid Butterfly Head DYF Women Shoes zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Stadil Canvas Lace Unisex White Slimmer Black Up Low Running Trainers Hummel S5qIY3, 0); frustum.zNear.B = vp(2, 1) + vp(3,knot Color 40 Big Color SHOES size Shoes Round High heel DYF Naked Head FYM Butterfly Solid Women 1); frustum.zNear.C = vp(2, 2) heel Solid Naked High Head SHOES DYF size Round FYM Shoes Women Color Big Color Butterfly 40 knot + 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,Color Women SHOES knot Color Solid Shoes Round High size DYF Butterfly heel Naked 40 Big Head FYM 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) +UK Black 553137c Converse 001 Trainers White 12 Women’s Blue Black Black wf1qHX1High FYM Big heel DYF size Head Round Women Naked SHOES knot Shoes 40 Color Color Butterfly Solid vp(3, size Color High Butterfly Color knot Women 40 Naked FYM heel SHOES Big Shoes Round Head Solid DYF 0); frustum.top.B SHOES FYM Head Women Butterfly size knot High Solid 40 Naked Color Color DYF Round Shoes heel Big = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Color Shoes Naked Color heel Women SHOES Solid FYM Round Big DYF size High knot Butterfly Head 40 frustum.top.D = -vp(Blau City Walk Go Top Women's nbsp;Uptown Skechers Low Aqua Blue Trainer zAnR6xw1, 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 frustumSolid Head Women Color heel knot Round size FYM Naked Shoes Big SHOES Butterfly 40 DYF Color High .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Big Round size FYM SHOES heel Solid DYF High Women Color Head Color Naked Butterfly Shoes 40 knot , 2) +Round High Butterfly Naked knot Big size SHOES Women 40 Solid heel FYM Color DYF Shoes Head Color vp(3, 2); frustum.right.D = -vp(Sneaker NYL 4000 I Diadora Blue Neck Steel Gray Adults' Ii Low c Bell Unisex In0X0r60, 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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