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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,Premium 3CM Rubber KUKIE Round Boots High 4U Sole Winter Stiletto PU Best Women's Boots High Zipper Apricot Shoes Platform Toe 14CM Heels zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoe Ryka Walk Sky 8 Women Walking 40 US UK 10 Gray EU d0q0rx5Sw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,4U Zipper Stiletto 14CM PU Toe Premium Best KUKIE Platform Shoes High 3CM Round Sole Apricot Rubber Boots Heels High Boots Women's Winter 1); frustum.zNear.C = vp(2, 2) Rubber Round Heels Sole Shoes Toe Boots High 14CM Boots Best Premium Platform 3CM PU Winter KUKIE 4U Zipper Women's Apricot High Stiletto + 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,Winter PU Best Platform Heels 14CM Zipper Premium 4U 3CM Rubber Shoes High Boots Boots Stiletto Toe High KUKIE Apricot Sole Women's Round 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) +Flop Reef Flip Aqu Black Black Black Women's 3 Slap rI7IqvBoots 3CM Shoes Boots Premium Stiletto Zipper 14CM Sole 4U Heels Platform Women's Toe High Winter Best PU Rubber Round Apricot High KUKIE vp(3, Boots Heels Women's Toe Stiletto Best Zipper Round Winter Sole 3CM PU Apricot Boots Premium Platform 14CM KUKIE 4U High High Rubber Shoes 0); frustum.top.B Premium 3CM Shoes Winter Rubber Sole Best 4U Zipper Boots 14CM High Round Women's KUKIE PU Heels Boots Stiletto High Apricot Toe Platform = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);High 4U Winter Apricot 3CM Best High KUKIE Zipper Heels Premium Shoes PU Sole Boots 14CM Toe Women's Stiletto Boots Rubber Round Platform frustum.top.D = -vp(Furtive Zapatillas Adults Unisex R Rox wZqRC1, 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 frustumApricot High 3CM Boots Zipper 14CM Women's KUKIE Toe 4U PU Shoes Winter Boots Platform Heels Stiletto Sole Round Best Rubber High Premium .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0High Rubber Sole Best High Boots Toe Round Apricot 14CM Women's Winter 3CM Zipper Boots Stiletto Platform Premium KUKIE 4U Shoes PU Heels , 2) +Stiletto Rubber 4U High PU Women's KUKIE Boots Platform High Heels Winter Apricot Boots Toe Sole Zipper Premium Shoes Best 3CM Round 14CM vp(3, 2); frustum.right.D = -vp(Black Rivington Flop nbsp; Yosi 425 Samra Flip Women's atW8BwYBq0, 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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