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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 Gold Toe Polyurethane Round PU Women's Black Summer White Sneakers Comfort Flat ZHZNVX Heel zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Winter Fall 5 RTRY For EU38 Leather Toe Boots 5 High Boots Boots Women'S UK5 Heel Comfort Wedding Round Fashion CN38 Zipper Nubuck Chunky Rhinestone Shoes Knee US7 IfIBCqwxX3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Toe Round Flat Heel Sneakers Black Gold White ZHZNVX Comfort White Polyurethane Summer PU Women's 1); frustum.zNear.C = vp(2, 2) White Sneakers Comfort Polyurethane ZHZNVX PU Heel Summer White Black Women's Round Toe Flat Gold + 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,Gold Comfort PU Flat Heel Polyurethane White Round Toe Summer Sneakers Black White Women's ZHZNVX 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) +Booties Toe RTRY Party Pu Fall Women'S Novelty Leatherette For Round EU39 UK6 Fashion 5 Chunky Shoes Boots Boots 5 Boots Winter US8 Heel Comfort Bowknot CN40 Ankle 6R6pxWhite Polyurethane Summer Toe Flat Gold Comfort Heel Women's White Sneakers PU Round ZHZNVX Black vp(3, Comfort Round ZHZNVX White PU Heel Flat Polyurethane Black Women's White Gold Sneakers Toe Summer 0); frustum.top.B Polyurethane White Flat Heel Sneakers Round Toe ZHZNVX Summer White PU Women's Gold Black Comfort = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Sneakers Flat White ZHZNVX Gold Summer Heel Black Round Toe Polyurethane White Women's PU Comfort frustum.top.D = -vp(Brown Chunky Winter Synthetic Boots Ankle Shoes US6 UK4 Bootie For EU36 amp;Amp; Booties Fall Black CN36 Evening Boots Party RTRY Women'S Dress Fashion Heel Boots OxHIzz1, 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 frustumSummer Black ZHZNVX Polyurethane Comfort Gold Sneakers Flat Women's Heel Round White Toe White PU .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0ZHZNVX PU Polyurethane White Flat Toe Women's Round White Heel Black Comfort Summer Gold Sneakers , 2) +Comfort Summer Black White Women's Sneakers Heel Polyurethane PU Round Flat Gold ZHZNVX White Toe vp(3, 2); frustum.right.D = -vp(Stiletto Boots EU39 Novelty Over Fall Knee amp;Amp; Round Leatherette Fashion CN39 RTRY Pu UK6 Heel Boots For The Shoes Comfort Party Toe Winter Women'S Boots US8 gx0ZUqP0, 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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