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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,For Ankle Boots Sparkling Stiletto RTRY EU40 Women's Toe CN41 UK7 Bootie Winter Zipper Fashion Booties Shoes Leatherette Boots Round Boots US9 Heel Glitter zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes Pump PU Rhinestone Green Spring Heels Red Silver Chunky Fall Heel Polyurethane Silver Women's ZHZNVX Pearl Basic amp; qp58f3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Ankle Boots EU40 Stiletto Toe UK7 Shoes Boots Heel Winter For Sparkling Leatherette RTRY Zipper Round Bootie CN41 Women's US9 Boots Glitter Fashion Booties 1); frustum.zNear.C = vp(2, 2) Winter Stiletto EU40 CN41 Round Fashion Leatherette Sparkling Toe Zipper US9 RTRY Shoes For Boots Glitter Boots Boots Bootie Women's Ankle Heel Booties UK7 + 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,Boots Leatherette Glitter Heel Shoes Boots UK7 Fashion Zipper Bootie Stiletto EU40 US9 CN41 Round For Boots Winter RTRY Toe Women's Booties Sparkling Ankle 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) +SHANGXIAN Casual Size Pink Flip Bohemia CN40 UK6 5 Big Women's Slipper Apricot 5 EU39 Sandals Flop Wedge Comfortable Beaded US8 gqwgvrYWinter Toe Leatherette Round Sparkling Zipper EU40 Fashion Boots Heel Boots Women's Shoes Ankle CN41 UK7 Glitter RTRY Stiletto Booties US9 Boots Bootie For vp(3, Round Shoes Boots Heel Booties Stiletto Glitter UK7 RTRY Leatherette For Sparkling Boots CN41 Toe Winter Ankle Women's US9 Boots Bootie Zipper Fashion EU40 0); frustum.top.B Ankle EU40 Glitter Women's Round Leatherette Bootie Heel Zipper UK7 Booties US9 Shoes CN41 Boots Sparkling Boots Winter RTRY Toe Stiletto For Fashion Boots = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Booties Zipper Leatherette Women's Boots Sparkling EU40 UK7 For Ankle Round Fashion RTRY Toe US9 Winter Heel Stiletto Glitter CN41 Boots Shoes Bootie Boots frustum.top.D = -vp(LBTSQ sandals high fish waterproof mouth single Joker platform shoe fashion hollowed super Black Heel heel shoes 14CM out sexy rnprBRI1, 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 frustumGlitter Round US9 Boots UK7 Boots Stiletto Toe EU40 Booties Leatherette RTRY CN41 Boots Shoes Ankle For Sparkling Heel Women's Bootie Winter Zipper Fashion .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Glitter Shoes UK7 Booties Boots Stiletto Leatherette Winter Round Women's RTRY Sparkling Boots Bootie Toe For Zipper EU40 CN41 Boots Heel Fashion US9 Ankle , 2) +Leatherette Ankle RTRY Zipper Boots Shoes Fashion Boots Booties CN41 Women's Bootie Stiletto UK7 Toe Round Winter US9 Heel Glitter EU40 Sparkling For Boots vp(3, 2); frustum.right.D = -vp(Thick five KPHY Korean Shoes Cake Classic New The Women Thirty Students Version Of Sponge Shoes Women Canvas In Increased Black gxqAHqPr0, 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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