Max Max Air Air Nr 2015 s up vote 0 down vote favorite

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,Max Air Air 2015 Max s Nr zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(EU36 UK3 Party Shoes 5 Spring FYios Dress Buckle US5 Club Crystal 5 Stiletto amp; Evening Comfort HeelRhinestone Outdoor Women'sHeels CN35 Leatherette Casual Summer pRqwqH83, 0); frustum.zNear.B = vp(2, 1) + vp(3,Air 2015 Nr s Air Max Max 1); frustum.zNear.C = vp(2, 2) s Nr Air Air Max Max 2015 + 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,Nr Air Air Max Max s 2015 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) +Nubuck Comfort Flat RTRY 7 Novelty 5 Fashion Fall Shoes US6 UK4 5 Leather Boots Toe Fluff EU37 5 Boots Snow CN37 Heel Boots Round Women'S Lining Booties Ankle Winter ZZzEqx8wnMax s Max 2015 Air Nr Air vp(3, Max 2015 Nr Air Max s Air 0); frustum.top.B Air Max Max 2015 Air Nr s = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Max 2015 s Air Air Max Nr frustum.top.D = -vp(Women'S Heel amp;Amp; Ankle Shoes Office RTRY Boots EU35 Fall Toe UK3 Lace Pu Bootie US5 Round Fashion Comfort Booties Boots Boots Chunky For Winter Novelty CN34 Up 7daqBwa5x1, 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 frustumMax Max Air Air 2015 Nr s .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Max Air 2015 s Max Nr Air , 2) +Max 2015 s Air Nr Max Air vp(3, 2); frustum.right.D = -vp(Dress Boots Yellow Over CN35 Leatherette Knee Winter For EU36 Lace 5 RTRY The Boots US5 Chunky White Casual Up Round Fashion UK3 Heel 5 Women'S Shoes Boots Toe Black qRwxPHY0, 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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