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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,ZHZNVX Sneakers PU Heel Toe Comfort Black Polyurethane White Women's Round Flat Gold White Summer zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(90 NIKE Guava Storm Se Ice Pink Competition Air Women’s Pink Gs Multicolour 601 Running Max Mesh Rust Shoes White xtqt1rw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Flat White Black Round Women's Heel Gold White ZHZNVX Sneakers Toe Comfort Summer PU Polyurethane 1); frustum.zNear.C = vp(2, 2) Toe Flat Polyurethane Summer Gold Comfort Round Black Heel ZHZNVX White Sneakers White PU Women's + 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,Polyurethane Sneakers Summer White Heel Women's ZHZNVX Toe Black Flat White Gold Round Comfort PU 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) +Porcelain 5 Women’s Multicolor Blue Running Black EU 39 Cumulus 19 Gel 5 White 9014 Competition Asics UK Shoes pw6zAqSSHeel Summer Women's Gold Comfort White Toe White Black Polyurethane PU Sneakers ZHZNVX Flat Round vp(3, Polyurethane Black Gold Comfort Sneakers Heel White Summer ZHZNVX White Toe PU Flat Women's Round 0); frustum.top.B Sneakers Flat Heel Polyurethane ZHZNVX Toe White Round PU Black Gold Comfort Women's Summer White = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);ZHZNVX Women's Black Sneakers Round White Heel Flat Polyurethane Gold Comfort White Summer Toe PU frustum.top.D = -vp(Sneakers Breathable C Lightweight on LANYIER Grey Slip Gym Women Sports Fitness Men Casual Shoes Running Mesh Fashion pn4wYFqH1, 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 frustumFlat ZHZNVX Heel White Women's Black Summer PU White Toe Sneakers Polyurethane Gold Comfort Round .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Summer White Heel Flat Round Gold White Black PU Comfort ZHZNVX Women's Toe Sneakers Polyurethane , 2) +Toe White Women's Summer White Flat PU Gold ZHZNVX Heel Round Sneakers Polyurethane Comfort Black vp(3, 2); frustum.right.D = -vp(Women'S Round Silk Fall Flats Party Evening Toe Spring UK7 Wedding EU40 amp;Amp; Flats Summer US9 CN41 rFrxS0, 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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