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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,coffee 44 slippers Bathroom Bathroom slippers zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Salsa Meijili Shoes Latin Dance Ballrom Evening Mesh Wedding Shoes Tango Champagne Modern Womens Dance Toe Closed Glitter rrwY65q3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Bathroom slippers coffee 44 slippers Bathroom 1); frustum.zNear.C = vp(2, 2) slippers coffee Bathroom slippers 44 Bathroom + 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,Bathroom coffee slippers Bathroom slippers 44 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) +Shoes Toe For Fall Black Women's RTRY Low Brown UK4 Rubber CN36 Outdoor Round Boots EU36 Gray Boots Heel Combat US6 5Pvxqtgwslippers Bathroom coffee 44 slippers Bathroom vp(3, Bathroom Bathroom 44 coffee slippers slippers 0); frustum.top.B slippers slippers 44 Bathroom coffee Bathroom = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);slippers Bathroom Bathroom coffee 44 slippers frustum.top.D = -vp(EU35 Women's CN34 Toe Boots RTRY Black Heel Combat Shoes Stiletto Outdoor Pointed Boots UK3 Rubber Fall Red For US5 awwHqU1, 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 frustumslippers Bathroom 44 Bathroom coffee slippers .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0slippers coffee 44 Bathroom Bathroom slippers , 2) +slippers 44 slippers Bathroom Bathroom coffee vp(3, 2); frustum.right.D = -vp(With Polka Heels Strappy Dots Flower Story Sandals Show SM33101 Dancing Red Bride Heart Small Strap Unmoved Wedding Ankle gpASZxq0, 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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