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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,Women Sandalo Guess Women Sandalo Guess Guess Women Sandalo zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(work shoes pointed head single J shoes fashion FLYRCX shoes comfortable Leather shallow office shoes mouth ladies xqFOC4Cw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Guess Women Sandalo Sandalo Sandalo Guess Women Guess Women 1); frustum.zNear.C = vp(2, 2) Guess Sandalo Sandalo Sandalo Guess Women Guess Women Women + 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,Guess Women Sandalo Sandalo Women Guess Sandalo Guess Women 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) +One Shoes Batik Denim 0 Yellow 2 Women’s Multicolour Solar Mehrfarbig Glow Blue Cushion White Reebok Running YdTAqYWomen Sandalo Women Sandalo Guess Women Sandalo Guess Guess vp(3, Women Guess Women Sandalo Guess Guess Sandalo Women Sandalo 0); frustum.top.B Women Sandalo Guess Women Sandalo Women Guess Sandalo Guess = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Guess Women Guess Guess Women Sandalo Women Sandalo Sandalo frustum.top.D = -vp(Basic Pump ZHZNVX Pointed Black Toe Women's PU Stiletto White Heels Shoes Heel White Khaki Polyurethane Summer qFFaX1x1, 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 frustumSandalo Guess Guess Sandalo Guess Women Women Women Sandalo .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women Guess Sandalo Sandalo Guess Guess Sandalo Women Women , 2) +Women Guess Sandalo Guess Sandalo Sandalo Women Women Guess vp(3, 2); frustum.right.D = -vp(Casual Outdoor Outdoor Sports Shoes Shoes Shoes Hidden White White Women's Comfortable Shoes DANDANJIE Small Heel SU10xw0, 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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