W Salomon GTX Salomon Salomon Loma Loma W Loma GTX W GTX 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,Loma GTX Salomon Loma W Loma W GTX Salomon GTX W Salomon zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(5 Combat Flat Comfort Calf Buckle CN37 Black Heel Round Toe 7 UK4 For Boots Shoes Fall US6 Mid Women's 5 Boots PU Boots EU37 5 RTRY Casual 8pXSwq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,W GTX Salomon Loma Loma Loma W W Salomon GTX Salomon GTX 1); frustum.zNear.C = vp(2, 2) Salomon Salomon Salomon GTX Loma GTX W W Loma GTX Loma W + 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,Salomon W Loma Loma GTX Salomon W W Loma GTX Salomon GTX 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) +Boots Boots Chelsea 34 Round Stretch Eu Heel Socks Wool Red Match Boots 7cm Size Boots Color Chunkly Stovepipe Toe 40 Stripe Women Knitted Dress t1waqW W Loma Salomon GTX Salomon Salomon Loma GTX W GTX Loma vp(3, W W GTX Loma Loma Salomon Loma GTX Salomon Salomon W GTX 0); frustum.top.B Salomon Salomon Loma GTX GTX Loma Salomon W W W Loma GTX = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Salomon Loma Salomon W W Loma Salomon Loma GTX GTX GTX W frustum.top.D = -vp(Black Wine Evening Party Pointed Wine Microfiber Shoes Heels Spring Women's ZHZNVX amp; Fall Heel Stiletto Strap Ankle Buckle Beige Toe amp; 6qCaH1, 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 frustumW GTX Salomon Loma Loma GTX Salomon W GTX Loma Salomon W .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0GTX GTX W GTX Loma Salomon W Loma Salomon W Loma Salomon , 2) +Salomon GTX Loma Salomon Loma GTX W GTX W Salomon W Loma vp(3, 2); frustum.right.D = -vp(Spring White 4in Stiletto Blue Comfort CN35 Pink Comfort Light US5 EU36 UK3 Black 5 PU Casual Walking 3 3in Buckle 5 Heel 3 Women'sSandals PzTE0E0, 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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