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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,Salomon Loma Loma GTX W W GTX GTX Salomon Loma Salomon W zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Transparent Nude Fine Women DYF Light Big 44 High size Sharp Shoes heel Black fU6nnRg3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Loma Loma GTX Salomon W Loma Salomon W W Salomon GTX GTX 1); frustum.zNear.C = vp(2, 2) GTX W W Salomon Loma GTX Salomon GTX Loma Salomon Loma W + 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,W Salomon GTX GTX Loma W GTX W Salomon Salomon Loma Loma 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) +Royal Women’s Rain 000 Trail Reebok Shoes LX Cloud Blue Running Glide White Z8ddqwGTX Salomon GTX Loma W W W Salomon Loma Salomon GTX Loma vp(3, GTX Salomon GTX W Loma Loma GTX Salomon W Salomon W Loma 0); frustum.top.B GTX GTX Salomon Salomon Loma W Loma Salomon Loma GTX W W = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Loma W GTX Salomon W GTX Salomon GTX Loma Loma Salomon W frustum.top.D = -vp(Dormet W Women’s 000 Tinnob Blue adidas Purtiz Volleyball Ligra 5 Shoes F7wx68qB1, 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 frustumSalomon Salomon Salomon W GTX W W Loma GTX Loma Loma GTX .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0GTX GTX Salomon Loma W Loma W Salomon Salomon GTX Loma W , 2) +GTX W Salomon W GTX Salomon Salomon Loma Loma GTX Loma W vp(3, 2); frustum.right.D = -vp(Ash Grey Grey Fire Reebok White Black Women’s 3D Running Zprint Coral Shoes cw7wAXYq00, 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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