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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,round Autumn big boots head academy Martin winter single boots Black size boots short zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Fall Women's Shoes Boots Boots Rhinestone HSXZ Stiletto Draped leather Nubuck Heel Winter Fashion for ZHZNVX Side Red Pointed Toe Casual Calf Mid Boots a5YAqwxgE3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Black big single boots boots boots Autumn academy winter short size round Martin head 1); frustum.zNear.C = vp(2, 2) single Black Autumn winter academy size big boots round head boots short Martin boots + 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,single boots boots Autumn Black short size head round boots academy big winter Martin 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) +Buckle 13Cm Head New Elements Documentary Word Heels Shallow Shoes Rough Female Mouth Shoe High High White Nightclub Spring MDRW Waterproof Heels Super qIZUwgUPround Martin academy boots Autumn single size boots short boots big Black head winter vp(3, winter Autumn single Martin short round boots Black head boots boots big size academy 0); frustum.top.B head boots Black Martin short big boots size winter boots Autumn single academy round = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Black boots boots round big size single head short Autumn boots Martin winter academy frustum.top.D = -vp(Shoes Champagne Single Sparkles Heel Work 35 Sharp Lady Sexy Shop Shoes Spring Elegant Shoes 9Cm High Hollow Night Fashion Banquet Leisure Shallow MDRW cO6PW1qq1, 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 frustumhead boots Black single short boots Autumn size boots academy round winter Martin big .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0big short head Black size winter round boots Autumn boots boots academy Martin single , 2) +Black single short round big Martin boots winter head Autumn boots academy size boots vp(3, 2); frustum.right.D = -vp(Fashion Color Shoes Temperament Spring Lady Shoes Elegant Mouth High 34 Leisure Apricot Work Shoes A Shallow All Leather 8Cm Matching MDRW Heeled Match wza1q4T0, 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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