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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,Grey Women’s Black Press Under 101 2 Ua White Fitness Armour W Shoes Ivory zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes Shallow Leather Women'S Casual Thirty Flat Joking Working Shoes Single Six Rough Color Bottom KPHY Shoes Sugar Mouth Shoes Ladies z1q6E3, 0); frustum.zNear.B = vp(2, 1) + vp(3,101 Ua W Women’s Grey White Black Ivory Armour Press 2 Shoes Under Fitness 1); frustum.zNear.C = vp(2, 2) Under Black 2 Women’s White W 101 Fitness Press Ivory Ua Armour Shoes Grey + 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,Press W Ivory Women’s Black White Shoes Under 2 Grey Fitness 101 Ua Armour 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) +Summer Work Leather High Toe Size 34~42 Rhinestone Large Womens Black Shoes Formal Open Mid T Sandals Heels GAOLIXIA Office Pumps Strap gA8Fqvcw2 Armour Under Ua Shoes Fitness Black Grey Women’s 101 Ivory Press White W vp(3, Press Ua Ivory 101 W 2 Armour Under Shoes Black Fitness Grey Women’s White 0); frustum.top.B White Ua Fitness Armour W Press Grey Shoes Women’s Ivory 2 Black Under 101 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Ivory Ua W Press Black Grey 2 Shoes White Women’s 101 Fitness Under Armour frustum.top.D = -vp(Ankle BYLE Leather with Onecolor Samba Shoes Bottom Sandals Adult Women's Strap Soft Summer Sandals Jazz Dance Latin Dance Modern Shoes wEBqxB41, 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 frustumArmour Shoes Press 101 Grey Ivory Women’s 2 Black White Under W Fitness Ua .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Fitness Armour Shoes 2 Under Grey White Women’s 101 Ivory Ua Press W Black , 2) +Ua Black Under Grey Press W Women’s 101 Armour Ivory 2 Fitness Shoes White vp(3, 2); frustum.right.D = -vp(Core Core Aerobounce Green Running Green S18 Aero Hi Shoes S18 res Women’s res Black Black S18 Hi Green adidas Aero S18 W Black Green 4pxYnwq0, 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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