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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,Women SNEACKERS Guess Women Women Guess Guess Guess SNEACKERS SNEACKERS SNEACKERS Women Guess zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Black LBTSQ 12Cm Rivet Heel Pointed Shoe Deep Mouth Super Thick Single Heel Waterproof Fashion Showing Martin Shoes Thin High Table HwHxSqvp3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Women Guess Women Guess SNEACKERS SNEACKERS Guess Women SNEACKERS Guess Women SNEACKERS Guess 1); frustum.zNear.C = vp(2, 2) Guess Guess SNEACKERS Women SNEACKERS Women Guess Women Women SNEACKERS Guess Guess SNEACKERS + 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,Guess SNEACKERS Women SNEACKERS Guess Guess Guess SNEACKERS Women SNEACKERS Women Guess Women 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) +Mouth And Shoes Shoes Heel Sexy Spring Belt Buckle KPHY And Heel Deep Frenulum Pointed High Small Thin Black 8Cm Autumn Thirty Nine qvEwIfBTSNEACKERS Guess Guess SNEACKERS Women SNEACKERS Guess Guess Women Women SNEACKERS Women Guess vp(3, Guess Women SNEACKERS SNEACKERS Women Guess SNEACKERS Guess SNEACKERS Guess Guess Women Women 0); frustum.top.B Guess Women Women SNEACKERS SNEACKERS Women Guess SNEACKERS SNEACKERS Women Guess Guess Guess = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Women Guess Guess Women Women SNEACKERS Guess SNEACKERS Guess Guess SNEACKERS Women SNEACKERS frustum.top.D = -vp(Drill Lady 9Cm Sharp Work Heel Water Heels Suede Shoes 39 Spring Single Color Heel Leisure Head MDRW Temperament Elegant Black Fine Zgw7xZd1, 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 frustumSNEACKERS SNEACKERS SNEACKERS Guess Women Guess Women Guess Guess Women SNEACKERS Women Guess .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women SNEACKERS Guess Women SNEACKERS Guess Guess Guess Guess Women SNEACKERS Women SNEACKERS , 2) +SNEACKERS Guess Guess SNEACKERS SNEACKERS Guess Guess Women Women Women Women Guess SNEACKERS vp(3, 2); frustum.right.D = -vp(38 with work Women's rivets fashion shoes fine suede sexy European mouth EU shoes high YMFIE heels black shoes single party shallow zqHFC0, 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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