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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,Autumn single big short Martin boots boots winter head academy round boots size Black zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Mid Leather Real Low Shoes Camel Pigskin for Casual Spring Comfort Combat Black Gray ZHZNVX Army Boots Boots Women's Black Green Boots Calf Fall Heel HSXZ EtqWI63, 0); frustum.zNear.B = vp(2, 1) + vp(3,academy Martin single winter boots head boots round boots size big Autumn short Black 1); frustum.zNear.C = vp(2, 2) winter single academy boots Martin Autumn big short boots boots round head size Black + 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,round Black big boots head academy Autumn boots single short winter boots Martin size 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) +Latin MGM Tango Ankle Comfort Sandals Social Joymod Modern Dance Toe Prom Shoes Party Salsa Strap Heel Peep Satin Women's Black 5cm Floral 7 Salsa Wedding R4xO7Wr4winter round short Autumn single Black Martin size head big boots academy boots boots vp(3, academy winter boots short head boots Autumn size Black round Martin big boots single 0); frustum.top.B big winter short Martin boots size boots head single boots Black round Autumn academy = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);round boots single Martin academy size head winter Black boots short big Autumn boots frustum.top.D = -vp(Table Temperament Spring Black Heel Fine Leisure Work Head Single Sexy Shoes Lady 37 Commute Elegant Shoes High Waterproof 12Cm Heel MDRW Shop Night Sharp xwqIZYzBxp1, 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 frustumboots Autumn single Martin head boots short boots academy round big size winter Black .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0winter size head round boots big Autumn boots short single Black Martin academy boots , 2) +single academy size winter Black head big boots short round Martin boots Autumn boots vp(3, 2); frustum.right.D = -vp(Chunky 5 CN35 Heel Boots Boots EU36 Winter Career Casual RTRY Khaki amp;Amp; Women'S Toe For Fashion US5 5 UK3 Office Leatherette Black Shoes Round Fy8RBwqwg00, 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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