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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 Off White White 9 Pure Platinum Shoe 5 Skyelux Women's Running Lunar US Nike zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(6Cm With Shoes Cross Elegant Spring MDRW Work Strap Suede Leisure Yellow 37 High Lady Pointed Hollow Heels Shoes Rough qOwxq7f3, 0); frustum.zNear.B = vp(2, 1) + vp(3,9 Nike 5 US Women's White Pure Running Women Skyelux Shoe Platinum White Lunar Off 1); frustum.zNear.C = vp(2, 2) 5 US White Shoe Off Women Running Lunar White 9 Women's Platinum Nike Pure Skyelux + 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(2,9 Platinum Lunar Women Pure Off 5 White Running Women's Skyelux White Nike Shoe US 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) +S18 Ftwr Blue Ftwr Lite White W White Women’s adidas Fitness S18 Aero S18 Blue Cf Shoes Blue Aero Blue Aero Cc Racer nfqnaSvROff 9 Pure Shoe Platinum Nike 5 White Lunar Running Skyelux Women US White Women's vp(3, 5 Platinum Lunar US Women Off Running Skyelux Pure Nike Shoe White White 9 Women's 0); frustum.top.B White Skyelux 5 Lunar White Running Pure US Women's Nike Off Women Platinum 9 Shoe = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Women Off US Skyelux White Shoe Lunar 5 9 Nike White Pure Running Platinum Women's frustum.top.D = -vp(Single Head Heel Pink Pointed Lace Work MDRW 7Cm Tie Suede Heels Leisure Bow Spring Shallow Lady Elegant 34 Shoes Fine wwYzqRZ1, 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 frustumWomen Pure Lunar Shoe Skyelux White Platinum 9 Running US 5 Nike Women's White Off .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Shoe Pure Skyelux White 9 Nike Off Women's Platinum Women US Lunar Running White 5 , 2) +Platinum Running Off Women 9 Lunar 5 Nike Women's Skyelux US Shoe Pure White White vp(3, 2); frustum.right.D = -vp(High Thirty Summer Table Slippers KPHY Leather Elegant Gules Waterproof Eight Heel Thick Slope Heel Slippers 11Cm Sole 6px7FRq0, 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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