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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,Off Women's Nike Running Pure Platinum White Shoe White Skyelux 9 5 US Lunar Women zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Blondo Pink Shoe Victoria Rain Waterproof Light Women’s Suede YprqnHY3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Platinum Pure Women 5 9 White Lunar White Running US Shoe Women's Nike Off Skyelux 1); frustum.zNear.C = vp(2, 2) Lunar Platinum Running White US Nike 5 Women's Off Shoe Skyelux 9 White Women Pure + 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,Nike Skyelux White 9 White Women Shoe 5 Women's US Platinum Off Running Pure Lunar 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) +Shoes Grey BW1100V1 Fresh Boot Balance Grey Foam Womens New OqgwYp5 Pure Off Women Shoe Women's 9 Lunar White White Running Skyelux US Platinum Nike vp(3, Women's US Platinum Pure White Women Shoe 9 Running Skyelux Lunar Nike 5 White Off 0); frustum.top.B White Pure Running Off White Women Skyelux Women's Lunar Shoe Nike Platinum 5 9 US = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Pure 9 Skyelux Off Women's Running White 5 Platinum Lunar Nike Women Shoe US White frustum.top.D = -vp(Womens Leather Ladies Willow Blue Casual Boots Darkwood Steel 1xOUw11, 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 frustumPure Lunar White 5 Platinum Nike White Running Off Women US Skyelux Women's Shoe 9 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0US Skyelux Pure Running Lunar Shoe White Women's Off Platinum White Nike Women 9 5 , 2) +Off White Women's 9 Platinum Shoe Nike Running Lunar Women US 5 White Skyelux Pure vp(3, 2); frustum.right.D = -vp(Shoe Light Victoria Blondo Suede Grey Waterproof Rain Women’s 4X7qwOnqH0, 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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