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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,White Winter Comfort Fall Red Polyurethane Women's Shoes Flat ZHZNVX Red Heel amp; PU Sneakers zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(for Shoe Summer Pool Aqua Beach Water Kid Shoes Surf Gray Swimming Slipper Socks Men Women Dry Home Diving Quick Barefoot Yoga for rqrSO73, 0); frustum.zNear.B = vp(2, 1) + vp(3,amp; Comfort White PU Heel Women's Red Winter Red Sneakers Fall Polyurethane ZHZNVX Shoes Flat 1); frustum.zNear.C = vp(2, 2) Red Shoes Comfort Sneakers amp; White PU ZHZNVX Women's Heel Fall Winter Flat Red Polyurethane + 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,ZHZNVX Winter amp; Heel Red Sneakers Comfort PU Polyurethane Red White Women's Fall Flat Shoes 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) +AIRAVATA Shoes Blue162 Lightweight Dry Beach Summer Athletic Water Breathable Sneakers Clogs Swimming Slip Quick 0n Women Hole for rxqrf1Flat Fall Sneakers Polyurethane ZHZNVX amp; Shoes Red Comfort White Women's Winter Heel PU Red vp(3, Red Shoes Winter PU Heel Women's Comfort ZHZNVX Flat amp; Fall Polyurethane White Red Sneakers 0); frustum.top.B Polyurethane Winter Red Red Fall White Heel Comfort Flat Women's Sneakers amp; PU Shoes ZHZNVX = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Flat Fall Sneakers Shoes amp; ZHZNVX Red Winter Comfort Women's Polyurethane Heel Red PU White frustum.top.D = -vp(Velvet Metal Spring Heel Shoes Pointed Single Seasons Low Thick Buckle Black KPHY Medium Heel Shoes Four Spring Heel Early Buckle xwTq5XY61, 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 frustumHeel Women's Polyurethane Shoes ZHZNVX White Fall Red amp; Winter Flat Comfort Red PU Sneakers .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Shoes amp; Polyurethane Sneakers Fall Heel White Winter PU Comfort Flat Red Red Women's ZHZNVX , 2) +Comfort Winter Heel Polyurethane Sneakers PU amp; Red White Fall Flat ZHZNVX Red Shoes Women's vp(3, 2); frustum.right.D = -vp(Slippers Embroidery Cool Scrub Beach Flat Leather Red Toe Shoes Leather Shoes Size Slippers 39 Eu Scrub Casual 35 Open Shoes Women wPxqrtPfp0, 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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