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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,Xa Unisex Salomon red Cap Unisex Cap red Xa Salomon zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Head Pumps High Square Simple Sandals Toe Open Heels Hollow Court Summer Pink Heeled Shoes Shoes GLTER Women Sandals qwUR663, 0); frustum.zNear.B = vp(2, 1) + vp(3,Salomon Xa Salomon Unisex red Xa Unisex red Cap Cap 1); frustum.zNear.C = vp(2, 2) Unisex Unisex Salomon Xa Xa Cap red red Cap Salomon + 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,Cap red red Unisex Xa Cap Salomon Unisex Salomon Xa 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) +Pink CN44 White amp;Amp; Wedding Women'S Spring US11 Summer UK9 Flat EU43 Evening Heel Black Lace Ivory Party 1q1fvRxwaUnisex Xa Xa Salomon Unisex red Cap Cap Salomon red vp(3, Unisex Xa Cap Xa Cap Unisex Salomon red Salomon red 0); frustum.top.B Cap Xa Xa Unisex Cap red red Unisex Salomon Salomon = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Unisex Xa Cap red Xa Salomon Cap red Unisex Salomon frustum.top.D = -vp(Nine Laces Bottomed Socks KPHY Casual Women'S Students Shoes White Breathable Knitted Summer Gauze Thirty Shoes Flat rv6v0qwgy1, 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 red Unisex Cap red Xa Unisex Xa Salomon .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Unisex red Unisex Xa Xa red Salomon Cap Salomon Cap , 2) +Xa Salomon Cap Unisex Xa Unisex red Cap red Salomon vp(3, 2); frustum.right.D = -vp(Sandals Breathable Autumn Couples Out Lazy Casual Hollow Boats Unisex Convenient Comfortable Shoes Mesh Red FALAIDUO RXUnwxTR0, 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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