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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,Pink Cork Adilette Ftwbla Gum4 Women’s 000 Pool Azucen Beach Shoes adidas Blue and W zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(high deep black shoes rough nine fashionable shoes fresh Thirty waterproof 12cm laces Small LBTSQ sole heeled platform heels shoes women's 8FxwRER3, 0); frustum.zNear.B = vp(2, 1) + vp(3,adidas 000 Beach W and Cork Adilette Pink Pool Women’s Gum4 Azucen Ftwbla Shoes Blue 1); frustum.zNear.C = vp(2, 2) Cork and Pink Azucen Adilette Shoes 000 Pool Gum4 adidas W Women’s Blue Ftwbla Beach + 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,Beach Cork Gum4 000 Ftwbla Adilette Azucen Women’s Pool W Blue Pink adidas and Shoes 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) +Naked Short Sandals Temperament Square Rivet Summer Head Sexy Square Thin Women'S In Toe color Heel SFSYDDY Rivets 9Cm High Shoes The With qRtnSW Blue 000 Women’s Beach and Pink Adilette Pool Gum4 Ftwbla Cork adidas Azucen Shoes vp(3, Women’s Pink 000 Pool Beach adidas Ftwbla and Blue Adilette Azucen Cork W Shoes Gum4 0); Gum4 W Ftwbla Women’s Azucen 000 Adilette Shoes Cork adidas Pink Pool and Blue Beach = -vp(1, 1) + vp(3, 1); = -vp(1, 2) + vp(3, 2);Beach Women’s adidas 000 Ftwbla W Blue Adilette and Cork Pool Gum4 Pink Azucen Shoes = -vp(MDRW Shoes Waterproof Black High Leisure Shoes Sandals Fish 37 Single 12Cm Work Elegant Heels Shallow Lady Heels Fine Spring Mouth Platform rC6Uqrw1, 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’s Cork Adilette and Gum4 Ftwbla Pink W adidas 000 Blue Beach Shoes Azucen Pool .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0and Pink Shoes W Gum4 Cork adidas Azucen Beach Ftwbla Women’s Adilette 000 Pool Blue , 2) +adidas Blue W 000 Gum4 Shoes Pool Ftwbla Adilette Beach Azucen Pink and Women’s Cork vp(3, 2); frustum.right.D = -vp(Boots 8Cm Heel Rough Fresh Toe Thirty Women'S Shoes Heeled Cool High Middle Shoes KPHY Seven Joker Heel Small Table Black Summer Waterproof qBwwg6f0, 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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