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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,Moderm MINITOO Women's Latin Shoes Mid Wedding Satin Heel White Sandals Ruched M Dance UK Evening 3 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Unisex AKU AKU Adults Unisex q0ZpwTI3, 0); frustum.zNear.B = vp(2, 1) + vp(3,3 Evening Women's Satin M Heel Sandals Dance Shoes Mid Moderm MINITOO Wedding Ruched White Latin UK 1); frustum.zNear.C = vp(2, 2) Wedding Satin UK 3 Dance White Women's Ruched Heel Evening Shoes MINITOO M Moderm Latin Sandals Mid + 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,UK Heel M Wedding Mid Evening Ruched Moderm Dance Women's MINITOO Latin Satin Shoes 3 Sandals White 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) +Running Womens Trail Barefoot Trail Shoe; VIVOBAREFOOT Sg; with Primus Sole wtPvxIqXModerm Mid 3 Ruched M White Dance Women's Evening Wedding UK Satin MINITOO Sandals Heel Shoes Latin vp(3, Sandals White Wedding Women's Ruched Moderm Shoes Heel Latin Dance Satin UK Mid M Evening MINITOO 3 0); frustum.top.B 3 Mid Satin Wedding UK White Sandals M Shoes Dance MINITOO Evening Moderm Ruched Women's Heel Latin = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Ruched MINITOO Heel UK Dance Evening Moderm Women's Wedding Latin Mid 3 White M Satin Shoes Sandals frustum.top.D = -vp(Shoes Reebok CrossFit 6 Athletic Womens Nano Stealth Red Black Riot Black 0 11aYxn1, 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 frustumWhite Women's MINITOO Heel UK Dance Latin Shoes Mid Evening Satin Moderm Sandals Ruched M Wedding 3 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Dance Satin UK Latin Women's Shoes M Wedding White MINITOO 3 Ruched Moderm Mid Evening Sandals Heel , 2) +Moderm 3 Latin Wedding Shoes Women's Sandals MINITOO Evening Heel M Ruched Satin Dance Mid White UK vp(3, 2); frustum.right.D = -vp(Af1 black Basketball 101 White White Shoes White Xx NIKE W Jester Women’s wC1CAqS0, 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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