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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,CN41 Booties Sparkling Winter Women's EU40 Boots Zipper Boots Ankle For Stiletto Shoes Leatherette UK7 Fashion Bootie Boots US9 Heel Round Toe Glitter RTRY zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Pop Mizuno Liberty Wave Orange Running W Shoes White Catalyst Purple Women’s 2 wPgZUSq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,For Zipper Stiletto Toe Winter EU40 Heel Shoes RTRY Bootie Boots US9 Leatherette Round Fashion Women's CN41 Booties Glitter UK7 Boots Boots Sparkling Ankle 1); frustum.zNear.C = vp(2, 2) RTRY Sparkling Winter Fashion Boots Ankle Stiletto Boots EU40 Zipper Boots CN41 For Bootie US9 Toe Heel Leatherette UK7 Women's Round Booties Shoes Glitter + 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,Winter Shoes Boots Ankle CN41 Boots Glitter Leatherette Sparkling Boots EU40 Zipper Round Bootie RTRY Booties Fashion UK7 For Stiletto US9 Women's Toe Heel 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) +Cleats Polarized 414 881543 Women's Blue Phantom 6 Soccer Hypervenom NIKE III FG q6fvCFor Ankle Glitter Stiletto Shoes Booties Leatherette EU40 Zipper Women's Boots Toe Sparkling Boots Fashion Heel US9 Round CN41 Winter Boots Bootie UK7 RTRY vp(3, Leatherette Shoes Heel Women's Boots Boots Stiletto CN41 Fashion Winter Boots Round RTRY Zipper EU40 Glitter For Bootie Toe UK7 Ankle Sparkling US9 Booties 0); frustum.top.B Bootie Winter EU40 CN41 For RTRY Women's Boots Shoes Zipper Stiletto US9 Glitter Toe Boots Boots Sparkling Round Booties Fashion UK7 Ankle Heel Leatherette = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);EU40 Glitter Women's Bootie Heel UK7 Shoes Zipper Leatherette Fashion CN41 Winter US9 For Round Boots RTRY Stiletto Ankle Toe Boots Sparkling Boots Booties frustum.top.D = -vp(NIKE Running White white Platinum Shoes Pure WMNS Lunarglide Competition 9 Women’s rwvRWXqgr1, 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 frustumWomen's US9 For Booties Fashion Ankle CN41 RTRY Boots Toe Boots Zipper Stiletto Bootie Round Glitter Sparkling Winter Shoes Heel Boots Leatherette EU40 UK7 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Toe RTRY For Winter Booties Boots Women's Stiletto EU40 Heel Glitter Round CN41 Shoes Zipper Boots Sparkling Bootie UK7 US9 Boots Ankle Fashion Leatherette , 2) +Women's For Bootie Sparkling Booties Boots Heel Winter Zipper Ankle Glitter Round Fashion Boots Shoes EU40 Boots US9 CN41 Leatherette RTRY Stiletto Toe UK7 vp(3, 2); frustum.right.D = -vp(urban Shoe Women's Red chalk black Crossfit Crossfit Primal Reebok Nano 0 Maroon 8 qzWIRx0, 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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