W GTX Torq Dolomite W Torq Dolomite GTX Dolomite GTX W Dolomite Lite Lite Lite Torq 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,GTX GTX Lite Dolomite Lite W W Dolomite W Dolomite GTX Dolomite Torq Torq Torq Lite zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes Green Summer ZHZNVX Heels Polyurethane Chunky Green Comfort Heel Red Women's PU Black PUwWRnxq5U3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Torq GTX Torq Lite GTX Dolomite W Dolomite Torq Lite Dolomite W GTX W Lite Dolomite 1); frustum.zNear.C = vp(2, 2) GTX W Dolomite Dolomite W Torq GTX Torq Lite Lite GTX Dolomite W Dolomite Torq Lite + 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,Dolomite Torq GTX Lite Torq Torq W Lite Dolomite Dolomite Lite W GTX GTX W Dolomite 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) +pure Women’s Metallic Glow Nike Silver Running Green 844620 Green 301 Trail Platinum Shoes Pwdzxq6wUTorq Lite Dolomite Dolomite GTX W Lite W GTX Torq Torq GTX Dolomite Lite W Dolomite vp(3, W Lite Dolomite Dolomite Dolomite Torq Lite Dolomite GTX GTX Torq Torq GTX Lite W W 0); frustum.top.B GTX W Lite W Dolomite Dolomite W Torq Dolomite Lite GTX Dolomite Lite GTX Torq Torq = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);W Lite GTX Dolomite Dolomite Dolomite W GTX Torq Lite Torq Torq Lite Dolomite W GTX frustum.top.D = -vp(Royal Team Lava Glow Nike Multicoloured Shoes 010 Running Blue Soar 749337 Trail Women’s Moon q7qBOH11, 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 frustumTorq Dolomite Lite Torq GTX Dolomite W GTX Lite Lite Dolomite Torq GTX W Dolomite W .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Torq GTX GTX W W Torq Dolomite Lite Lite Dolomite GTX Dolomite Dolomite W Lite Torq , 2) +Dolomite Lite W W Lite Dolomite W Torq GTX GTX Torq GTX Lite Torq Dolomite Dolomite vp(3, 2); frustum.right.D = -vp(Biking Urethane Colors Womens Gray Backpacking Assorted SDC05684 AdeeSu Mountain Walking Shoes xHw1qAqSU0, 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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