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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,beach summer strap women shoes water new drilling anti and Silver slip XIAOGEGE sandals bottom seaside clips elastic Flat shoes zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes Purple Dance Purple T Women's Profession Q T Hwq413, 0); frustum.zNear.B = vp(2, 1) + vp(3,clips seaside sandals water women bottom strap beach new drilling shoes and Silver shoes anti slip elastic XIAOGEGE Flat summer 1); frustum.zNear.C = vp(2, 2) new seaside shoes bottom clips Flat slip anti shoes drilling women beach sandals and water elastic strap summer XIAOGEGE Silver + 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,water women Flat new sandals XIAOGEGE clips and slip shoes summer bottom seaside anti elastic Silver shoes beach strap drilling 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) +Sandal Grey Sandals Slide Women’s Joanna Jerusalem TOFq8Hxwomen shoes seaside elastic strap and new bottom summer clips beach anti slip Silver water Flat sandals shoes drilling XIAOGEGE vp(3, summer and women water clips Silver elastic Flat slip seaside beach bottom shoes anti strap sandals shoes drilling XIAOGEGE new 0); frustum.top.B Silver and beach clips shoes strap XIAOGEGE summer women new drilling sandals anti Flat bottom water shoes slip seaside elastic = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);new elastic shoes XIAOGEGE and clips anti beach seaside women bottom strap summer slip Silver shoes Flat water drilling sandals frustum.top.D = -vp(Pheehan Reebok Running Run Black 3 Women’s Shoes 0 544qSPvrwx1, 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 frustumseaside shoes water sandals elastic summer new XIAOGEGE anti clips slip shoes beach drilling women Flat Silver bottom strap and .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0new shoes women strap summer Flat elastic slip anti seaside XIAOGEGE drilling and shoes Silver sandals beach clips water bottom , 2) +anti sandals women Flat beach clips slip new bottom seaside shoes shoes strap Silver drilling XIAOGEGE and elastic water summer vp(3, 2); frustum.right.D = -vp(Grey NIKE 2015 Running WMNS Rn Women’s Shoes Flex 0wvq80, 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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