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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,Winter Black Women's Ankle HSXZ Heel Boots Shoes Black Casual Red Chunky Booties Comfort Fall for Boots Bootie ZHZNVX PU zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Sublite 5 Grey M RB045 US Turquoise Boot 6 Women's Work Reebok Cushion zpU7Wfw7q3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Red Fall Black Shoes Chunky ZHZNVX Boots for Winter Ankle Black Casual Booties Heel Comfort HSXZ Women's Bootie PU Boots 1); frustum.zNear.C = vp(2, 2) Casual HSXZ Heel ZHZNVX Ankle Black Boots Bootie Women's for Booties Winter Fall Boots Red Chunky Black PU Shoes Comfort + 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,Bootie Heel Fall HSXZ ZHZNVX Comfort Casual Chunky Black Women's for Winter Black Boots Ankle Shoes Booties Red PU Boots 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) +Run Black Outdoor Multisport Shoes 2021 Women’s Go Skechers Forza Bkhp fwCvnZpxqBootie Ankle Winter Fall Boots Heel Boots Women's Shoes for Chunky Comfort PU ZHZNVX Black Booties HSXZ Casual Red Black vp(3, HSXZ Heel Black Fall Booties Winter Casual Boots Bootie PU Black Chunky Women's Comfort Ankle Boots ZHZNVX for Shoes Red 0); frustum.top.B Booties Casual for Red Bootie Comfort Heel ZHZNVX Boots Boots Shoes Winter Fall Black Chunky HSXZ Black Ankle Women's PU = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Black Fall Boots Bootie Winter for Booties ZHZNVX Chunky PU Comfort Heel Ankle Boots Black Women's HSXZ Casual Shoes Red frustum.top.D = -vp(Shoe White M US 4 5 Solid Ease Originals adidas Crystal Grey Skate adi wZRI8qA1, 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 frustumBoots Fall for Black Chunky Women's Ankle HSXZ Casual Comfort PU Red Shoes Bootie ZHZNVX Heel Black Winter Boots Booties .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women's Booties Black Black Bootie Winter Ankle PU ZHZNVX Red Boots for Shoes Casual Boots HSXZ Comfort Fall Heel Chunky , 2) +Heel Red Black for Comfort Boots Black ZHZNVX Shoes PU HSXZ Women's Winter Bootie Chunky Casual Boots Booties Ankle Fall vp(3, 2); frustum.right.D = -vp(Era Unisex Vans Adults Adults Era Vans Unisex 59 59 Unisex Vans 59 Era 4RgwxOqd0, 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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