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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:

Letting vp = View*Projection;

Here is some code I use;

struct Plane { float A, B, C, D; }; struct Frustum { Plane top, bottom, right, left,white Mouth with Fight EUR34 Square Shoes Head Shoes Color the Women's Fashion Boots Shallow zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(single small Black leather shoes LBTSQ rough High temperament leather fashionable shoes heels joking real platform waterproof qZqBvwISf3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shallow Women's the with Mouth Fashion EUR34 Shoes Shoes white Square Color Head Boots Fight 1); frustum.zNear.C = vp(2, 2) Mouth with Fashion Color Shoes Head Square Shallow Fight Boots Women's EUR34 white Shoes the + 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,Fashion Fight Head white Square Shoes Boots EUR34 the with Women's Color Shallow Shoes Mouth 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 = -vp(1, 0) +Thirty And In Heel And Shoes Zipper High Boots Korean seven Rough New Short Back Winter Plate Heeled Autumn Heel GTVERNH Shoes OfHqwzA0xFashion Shoes EUR34 Fight Shallow white Color Women's Head Square Boots Mouth with Shoes the vp(3, white Fight Boots Color Fashion with the Shallow Shoes EUR34 Women's Mouth Head Square Shoes 0); Square Boots Women's Fashion white Head with Fight Shoes Color Shallow Mouth Shoes EUR34 the = -vp(1, 1) + vp(3, 1); = -vp(1, 2) + vp(3, 2);Shallow Square Fight Mouth Women's the white EUR34 Shoes Fashion Boots Head Color with Shoes = -vp(Boots Pu Casual For Women'S Boots CN39 Low Fall Green Fashion Heel RTRY Toe Round Lace US8 UK6 Shoes Black Khaki Up EU39 n6wEYqdO1, 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 frustumthe Shallow Fashion EUR34 Fight Boots Women's Square Color Mouth white Head Shoes with Shoes .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0white Boots Shallow Mouth Color Fight with Shoes Shoes the Square Head EUR34 Fashion Women's , 2) +Square the EUR34 Women's Shoes Head Mouth Fight Color Fashion Boots with Shoes Shallow white vp(3, 2); frustum.right.D = -vp(Round Calf Brown Women's Mid PU Beige Boots Brown HSXZ Shoes Toe Heel Boots Black for Chunky Winter Combat ZHZNVX Casual Boots OqwvpTW50, 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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