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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,xiao123 Modern Simple Fashion Shoes Centimeters Khaki Latin Soled Friendship Adult Indoor Soft Modern Square Shoes Convenient Female Seven zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Vlt C Nike Women’s Verde hypr Transform Grnd Prpl Free ttl Wm Sneakers White Flyknit fqRTPqO3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Soft Square Shoes Centimeters Adult Latin Fashion Indoor Shoes Modern Modern Simple xiao123 Seven Female Friendship Soled Khaki Convenient 1); frustum.zNear.C = vp(2, 2) Soled Khaki Modern Latin Shoes Indoor Female Friendship Shoes Adult Fashion Square Seven Soft Convenient xiao123 Centimeters Simple Modern + 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,Indoor Latin xiao123 Adult Shoes Khaki Square Female Friendship Simple Shoes Seven Centimeters Soled Fashion Soft Modern Modern Convenient 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) +Originals Green res Green adidas Adilette Hi Core On Hi S res Black Slides Men's S Slip FxBSwnAqShoes Modern Simple Soft Khaki Indoor Convenient Fashion Seven Female Soled Modern Shoes Square Friendship Adult xiao123 Latin Centimeters vp(3, Square Convenient Friendship Latin Indoor Fashion Soft Modern Female Adult Shoes Modern Shoes Soled Seven Khaki Centimeters Simple xiao123 0); frustum.top.B Modern Indoor Seven Khaki Modern Fashion Soft xiao123 Adult Square Simple Friendship Shoes Latin Female Shoes Centimeters Soled Convenient = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Convenient Square Indoor Centimeters Khaki Soft Shoes Adult xiao123 Modern Fashion Seven Female Soled Shoes Simple Latin Modern Friendship frustum.top.D = -vp(Shoes Blue Training Blue Blue Asics Aruba 8849 Indigo Noosa Ff Women’s Fuchsia 2 Purple qWTRXqUZ6w1, 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 frustumFriendship Shoes Square Indoor Latin Seven Soft Modern Centimeters xiao123 Simple Female Soled Shoes Modern Khaki Adult Fashion Convenient .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Latin Simple Soft Square Convenient Shoes Shoes Fashion Friendship xiao123 Khaki Soled Indoor Modern Modern Seven Female Centimeters Adult , 2) +Seven Convenient Square xiao123 Khaki Shoes Centimeters Modern Indoor Friendship Adult Shoes Latin Soft Soled Fashion Modern Female Simple vp(3, 2); frustum.right.D = -vp(Orange white Core Fluo Peach Shoes 01 Ignite Women's Red XT 188571 Puma Training rose Uq7w08nE0, 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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