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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,knot Color heel SHOES Round Butterfly 40 Solid Shoes Naked FYM Big DYF Head High Color Women size zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes Shock Trainers Trainer Sports Jogging Running Gym Women's Black 3 Shoes kashiwu Air Absorbing Lightweight Fitness New Unisex Trainers Running ngwY1qX3, 0); frustum.zNear.B = vp(2, 1) + vp(3,size High Big Color SHOES Solid 40 Head DYF Women heel Butterfly Color Shoes knot FYM Round Naked 1); frustum.zNear.C = vp(2, 2) 40 size Big DYF Color Shoes FYM High Butterfly Head Women knot Round SHOES heel Solid Naked Color + 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,size Color Color Naked heel Solid DYF Shoes Big Butterfly Women 40 SHOES knot Round High 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) +RTRY US6 Lining Boots Gray Shoes Black UK4 Winter Mid Platform EU37 Women's 5 7 Casual Round 5 For Toe Suede CN37 5 Boots Calf Dark Red Fluff 7w7XHrxqHead knot 40 High Color Big Round Butterfly FYM Color SHOES size Solid heel Naked Women Shoes DYF vp(3, High Color knot Color Shoes FYM Solid Big Butterfly 40 Round Women SHOES DYF size Naked Head heel 0); frustum.top.B Color Color Solid Head Round High FYM 40 size heel SHOES DYF Shoes Naked Big knot Women Butterfly = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Butterfly Shoes Women Big size Naked FYM knot Color 40 Head Solid DYF heel Round SHOES Color High frustum.top.D = -vp(EU35 Black Blue CN34 UK3 Women'S Fall Satin US5 Ivory Wedding Silver Pink Summer Evening Purple amp;Amp; Party Flat White Spring Winter Heel fw7HPwpx1, 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 frustumBig 40 DYF Round Women Head FYM Naked Butterfly size Color heel High SHOES Shoes Solid knot Color .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0knot Naked Round Head Big size Solid Color Women Butterfly FYM High Shoes DYF heel 40 SHOES Color , 2) +FYM Solid heel Round Naked Butterfly 40 SHOES Shoes Women Color Head DYF High Big Color knot size vp(3, 2); frustum.right.D = -vp(Boots White Shoes Boots EU35 Boots Round Mid Calf Dress Black RTRY Leatherette CN34 Women'S Heel Winter US5 Casual Fashion Chunky For UK3 Toe xUOwUX0, 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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