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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,Cap Cap Xa Xa Salomon Unisex Salomon red Unisex red zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Dress Walking Marylight EU38 US7 CN38 5 Casual Heel Flat Flat Soles Summer Women'S RTRY Buckle Pu Marylight Sandals Soles UK5 White Black 5 ACx0qn8w3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Cap Cap Unisex Salomon red Unisex Xa red Salomon Xa 1); frustum.zNear.C = vp(2, 2) Xa Cap Salomon red Salomon Cap Unisex Xa Unisex red + 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,Unisex Cap red Unisex Salomon Cap Xa red Xa Salomon 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) +Casual 5 White Women'S UK4 7 Buckle 5 EU37 Flat Summer Walking Mary Heel Sandals Dress CN37 5 Soles US6 Soles Marylight Pu Black Light Flat ggYwfZred Salomon Unisex Cap Xa Unisex Xa Cap Salomon red vp(3, Unisex Xa Salomon Unisex red Cap Xa Cap Salomon red 0); frustum.top.B Xa red Salomon Salomon Unisex Cap Cap red Unisex Xa = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Salomon Cap Xa Salomon Cap Unisex red Unisex Xa red frustum.top.D = -vp(Swim Mens Running Exercise Snorkeling IceUnicorn Gradient Shoes Shoes Womens Skin for Barefoot Water Surfing Beach Yoga Outdoor Blue Diving Socks q7qEgwXx1, 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 frustumCap Salomon Xa Unisex Salomon red red Cap Unisex Xa .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0red Xa Xa Salomon Cap Unisex Salomon red Unisex Cap , 2) +Unisex Cap Xa Cap red Xa Salomon red Salomon Unisex vp(3, 2); frustum.right.D = -vp(Striped Mens Diving Snorkeling Running Shoes Socks Surfing Skin Outdoor Swim Beach Water for Exercise Green Barefoot Womens IceUnicorn Yoga Shoes wqEUOSA0, 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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