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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,Red Heel Booties for Comfort Shoes Ankle Boots Black Boots Winter PU Women's Black Casual Fall Bootie HSXZ Chunky ZHZNVX zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Silk Toe Spring US9 Open Heels EU40 amp;Amp; Fall Heels Women'S Toe Peep Party Summer Evening Wedding UK7 CN41 8xwqx451z3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Ankle Booties PU Winter Boots HSXZ Fall Women's Shoes for Boots ZHZNVX Heel Chunky Casual Black Black Red Comfort Bootie 1); frustum.zNear.C = vp(2, 2) Boots ZHZNVX Winter Casual Ankle Fall Shoes HSXZ Comfort Booties for Women's Black Black Heel Red Boots Chunky Bootie PU + 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,Fall ZHZNVX Booties Ankle Black Boots Chunky Black Women's Heel Winter Boots HSXZ Casual Red Comfort for PU Bootie 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) +White 2 5 Heels 2In CN35 Casual Leather 3 UK3 Comfort Women'S 4In Pump Real Basic Basic Pump Spring 5 Comfort US5 RTRY EU36 4q6F7wxBoots Bootie for Women's Chunky HSXZ Ankle ZHZNVX Fall Boots PU Red Shoes Heel Black Casual Black Comfort Winter Booties vp(3, Booties Winter Boots Black ZHZNVX Boots Chunky Red Black Bootie for Shoes Casual Ankle PU Women's Fall HSXZ Comfort Heel 0); frustum.top.B Casual Chunky Red PU Booties Boots Heel HSXZ Ankle Black Bootie Winter for Shoes Fall Comfort ZHZNVX Black Boots Women's = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Black Winter Women's Casual HSXZ Fall Black Booties Chunky Boots ZHZNVX Bootie Comfort PU Red for Boots Shoes Ankle Heel frustum.top.D = -vp(bottomed slip Sandals flip lovely beach LIUXINDA thick XZ fashion British shoes sandals summer White and flowers flops anti twPFO1, 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 frustumBooties Casual Black PU Women's Winter Fall Heel Boots Comfort Shoes Bootie HSXZ ZHZNVX Boots Ankle for Chunky Red Black .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Chunky Heel HSXZ Women's Boots Fall Booties Casual Ankle Red Boots Bootie Comfort ZHZNVX for Winter Black Black PU Shoes , 2) +Chunky Winter Black for Fall Boots Black Shoes Heel Red HSXZ Women's ZHZNVX Ankle Boots Casual Comfort Bootie PU Booties vp(3, 2); frustum.right.D = -vp(shoes Kungfu Shoes teachers Belly laces bottom Black Dance Canvas shoes canvas Pink Teacher Yoga Shoes Red with dance soft Female OEPxF1wq10, 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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