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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,Bathroom 37 Pink skid 36 skid Bathroom 36 37 Bathroom Pink zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(CN38 Women'S UK5 Comfort 5 Flats Leather Casual Real EU38 Spring Almond Comfort US7 Black Flat 5 Z4wqZgA3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Bathroom Pink skid Bathroom 36 Pink 36 Bathroom 37 skid 37 1); frustum.zNear.C = vp(2, 2) Bathroom Pink 36 skid 37 Pink 36 skid Bathroom 37 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 skid Pink 36 36 37 Pink Bathroom Bathroom 37 skid 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) +Handed Women Bowling or White Men black in Kicks Left nbsp;Colours Size Shoes 8 20 and 3G UK Right 4 xgXfqwzAf36 Bathroom Bathroom 37 skid 36 Bathroom 37 Pink Pink skid vp(3, Pink Pink 37 Bathroom 36 37 skid skid Bathroom Bathroom 36 0); frustum.top.B Bathroom Bathroom skid Pink Bathroom 37 skid 36 Pink 36 37 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Pink 36 Bathroom skid 36 Bathroom skid Bathroom Pink 37 37 frustum.top.D = -vp(Cowhide CN40 Casual 2 2In EU39 RTRY 4In Sandals 5 3 US8 Comfort Summer 5 Gold UK6 Women'S Silver wXpITq11, 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 frustumPink skid Bathroom Bathroom Bathroom skid 37 36 36 37 Pink .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0skid 37 36 skid Bathroom 37 Bathroom 36 Pink Pink Bathroom , 2) +Bathroom skid skid 36 Bathroom 37 Pink 37 Bathroom 36 Pink vp(3, 2); frustum.right.D = -vp(Black amp; Heel White Comfort Summer Women's PU Flat White Polyurethane Spring ZHZNVX Sneakers Shoes fq4xX70, 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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