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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,round Black single academy big size boots winter boots Autumn short head Martin boots zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Flex Women's Sky Cross Trainer Polar Shoes Yoga Ahnu 6axCZwnqq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,round short head boots Autumn Martin single Black big boots size winter academy boots 1); frustum.zNear.C = vp(2, 2) Autumn Martin boots academy round boots head short big Black single size winter boots + 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,short boots boots size boots single big Martin round winter Black head Autumn academy 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) +Sling Flip Metallic Silver Yoga Women's 2 Sanuk Flop 86xFwnboots Martin boots academy single winter size round head big boots Autumn short Black vp(3, boots boots short single academy Black Martin winter boots round size head Autumn big 0); frustum.top.B round winter Autumn big Martin boots single size short academy boots Black boots head = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);short Martin winter Black academy boots round single big boots boots size head Autumn frustum.top.D = -vp(819151 Blanco Women Nike Black 001 White Fitness Rnaxzv1, 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 frustumacademy size big single boots winter boots Martin head boots short round Black Autumn .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0head Autumn Black size round boots short big boots winter academy Martin single boots , 2) +single Martin short round winter size Black Autumn boots boots academy big head boots vp(3, 2); frustum.right.D = -vp(Diadora Fluo Adult Green Special Unisex 170549 97002 rPpcHqP0, 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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