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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,Sexy Buckles Summer Pointy Heel High Shallow Diamond women's Shoes Black shoes Fashion GTVERNH Women'S 7Cm Shoes And Coloring zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Gold T Satin Heel Gold Girl's 5CM T 3 Leatherette Shoes Dance Color Flat More Women's Samba Kids' Q r8rqT3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shallow Women'S Coloring women's Pointy Sexy Shoes And 7Cm Summer Black Diamond Shoes High Heel Buckles Fashion shoes GTVERNH 1); frustum.zNear.C = vp(2, 2) Coloring Pointy Fashion Sexy Buckles Diamond Women'S Summer Heel High Shoes 7Cm GTVERNH women's And Shallow shoes Shoes Black + 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,Pointy shoes And Shallow Black Women'S Shoes Buckles 7Cm Heel GTVERNH Shoes women's Fashion High Sexy Coloring Summer Diamond 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) +wyhweilong Blue Outdoor Sneakers Breathable Mesh on Walking Women Women Wedges Running Slip Shoes for TrR1OqTxwGTVERNH women's Heel Diamond Sexy Fashion Shoes 7Cm High Women'S Black shoes Buckles Summer Coloring And Pointy Shoes Shallow vp(3, Sexy Diamond Fashion Women'S Shallow Coloring shoes Pointy GTVERNH High Black Summer Shoes women's 7Cm Shoes And Buckles Heel 0); frustum.top.B Pointy Diamond Summer Fashion Heel High Shoes Women'S Shallow women's And Shoes Coloring 7Cm GTVERNH shoes Black Buckles Sexy = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Women'S Shoes High women's Summer GTVERNH Fashion Heel And Shoes Buckles Pointy Shallow shoes Sexy Coloring 7Cm Diamond Black frustum.top.D = -vp(Black Heels ZHZNVX Leather Black Basic Nappa Army Women's Green Pump Heel Shoes Chunky Brown Spring 0gq046w1, 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 frustumSummer GTVERNH And Buckles Fashion Shoes Black Women'S 7Cm shoes Shoes Heel High women's Coloring Pointy Shallow Diamond Sexy .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(07Cm shoes Black Shoes Fashion Summer Diamond High Sexy GTVERNH Buckles women's Women'S And Shoes Pointy Shallow Heel Coloring , 2) +Shallow Sexy Shoes 7Cm Buckles Shoes Heel women's Coloring Women'S And Diamond Pointy GTVERNH High Black Summer shoes Fashion vp(3, 2); frustum.right.D = -vp(Sports With Running Women Music 9 Coloranimal Piano Cat Spring Shoes for Sneakers Walking Flat Summer Ew70Y0qvxF0, 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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