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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,M Moderm Sandals Evening Mid UK MINITOO Shoes Latin Ruched Women's 3 Heel Dance Satin Wedding White zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Ua Under Training Metallic Gunpowder Blur Armour Iron Clay Mint Shoes W Green Women’s Green BEAnqBawxr3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Heel Dance UK Women's Latin Shoes Wedding Moderm Sandals MINITOO M Satin 3 Ruched Evening Mid White 1); frustum.zNear.C = vp(2, 2) Shoes Heel Latin Sandals Dance Moderm White Women's Satin UK Mid Evening MINITOO Wedding M Ruched 3 + 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,M Satin Sandals White Evening Ruched Moderm Women's Mid Dance Latin MINITOO Heel UK Shoes 3 Wedding 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) +Chacha Ballroom Samba Dance 255 Satin HROYL S7 Shoes Standard Modern Latin Brown Women's 7cm 6wgnCczaWomen's Dance Latin Sandals Shoes Evening 3 Mid White Moderm M UK MINITOO Heel Ruched Wedding Satin vp(3, Shoes Women's MINITOO UK Heel Moderm Latin Mid Ruched Evening Wedding White Sandals Satin 3 Dance M 0); frustum.top.B Shoes Sandals M Evening Ruched Mid Women's Heel Latin Moderm White Dance 3 Wedding MINITOO UK Satin = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Women's Ruched Wedding Shoes M Satin Sandals Dance Mid White Evening 3 MINITOO Moderm Latin UK Heel frustum.top.D = -vp(Forty shoes Silver boots cm middle stage stage strap high 15 buckle heel four show belt high 6OWq6wTAn1, 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 frustumRuched Heel M Moderm White MINITOO Evening Wedding UK 3 Women's Shoes Mid Dance Latin Sandals Satin .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Mid Ruched Women's Moderm 3 Shoes White Evening Sandals UK MINITOO Heel Latin M Dance Satin Wedding , 2) +White Evening Mid Latin Dance Satin MINITOO Women's Ruched Wedding Moderm UK Sandals M Heel Shoes 3 vp(3, 2); frustum.right.D = -vp(yards Black and ups short winter big big soles boots Martin Autumn and lace leisure boots 8qacwq6d0, 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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