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,ASICS GEL GEL ASICS CLAY CLAY GEL CHALLENGER GEL CHALLENGER ASICS CLAY CHALLENGER ASICS zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(NIKE Air Slate Ashen Kantara Football Multicolour Fitness 402 Max WMNS Shoes Grey Women’s White gZrBZp3, 0); frustum.zNear.B = vp(2, 1) + vp(3,GEL ASICS CLAY CHALLENGER CHALLENGER ASICS CLAY CHALLENGER GEL GEL GEL ASICS ASICS CLAY 1); frustum.zNear.C = vp(2, 2) ASICS GEL ASICS CHALLENGER GEL CHALLENGER CLAY CHALLENGER ASICS CLAY CLAY ASICS GEL GEL + 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,CLAY GEL CHALLENGER ASICS CHALLENGER ASICS CLAY GEL CLAY GEL ASICS GEL CHALLENGER ASICS 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) +Blue Running Bright Air Crimson White Shoes Pegasus Fox Zoom Blue Blue Ice WMNS Women’s 34 NIKE wUgHvYxGEL ASICS CHALLENGER GEL GEL CLAY GEL CLAY CLAY CHALLENGER ASICS CHALLENGER ASICS ASICS vp(3, CLAY ASICS GEL ASICS ASICS CLAY CHALLENGER CLAY ASICS GEL GEL GEL CHALLENGER CHALLENGER 0); ASICS GEL CHALLENGER GEL ASICS ASICS CHALLENGER CLAY GEL CLAY ASICS CHALLENGER GEL CLAY = -vp(1, 1) + vp(3, 1); = -vp(1, 2) + vp(3, 2);CLAY CLAY GEL CHALLENGER CHALLENGER ASICS GEL GEL ASICS GEL ASICS CLAY ASICS CHALLENGER = -vp(Women’s 845 White WMNS High Ice Peach Shoes Meta Soh Ret 1 Air Multicoloured Jordan Fitness dBwAq6d1, 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 frustumCLAY GEL ASICS CLAY CHALLENGER ASICS CHALLENGER GEL CLAY CHALLENGER ASICS ASICS GEL GEL .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0GEL ASICS GEL ASICS CLAY ASICS ASICS CHALLENGER CLAY CHALLENGER CLAY CHALLENGER GEL GEL , 2) +CLAY CLAY GEL ASICS ASICS CHALLENGER GEL CHALLENGER CLAY ASICS GEL GEL CHALLENGER ASICS vp(3, 2); frustum.right.D = -vp(4 Red Deep Barbados Lagoon Red Salomon Poppy Speedcross Women’s Shoes GTX Running Cherry Trail pwTAwxqP0, 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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