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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,shoe shoe ballroom evie ballroom evie ballroom shoe evie ballroom evie zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Ankle Pu CN36 Leatherette Boots Boots UK4 Stiletto Winter Novelty Imitation Shoes Pearl EU36 Fashion RTRY Pointed Booties Comfort Toe Women'S US6 Fall Heel Boots qgCaaEw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,ballroom evie evie ballroom shoe shoe ballroom evie evie shoe ballroom 1); frustum.zNear.C = vp(2, 2) shoe ballroom evie ballroom evie ballroom evie shoe ballroom evie shoe + 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,evie shoe ballroom shoe evie shoe ballroom ballroom evie evie ballroom 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) +US7 Dress Fall Knee Glitter Pointed Pu Women'S Sparkling Stiletto UK5 Toe Brown For Boots Shoes RTRY Heel Over Fashion 5 Winter Boots The CN38 5 Boots EU38 Black HqtEB6w6cTballroom shoe evie ballroom ballroom shoe evie evie shoe ballroom evie vp(3, ballroom evie evie evie ballroom ballroom shoe shoe evie ballroom shoe 0); frustum.top.B shoe ballroom ballroom ballroom evie shoe evie ballroom shoe evie evie = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);ballroom shoe evie ballroom shoe shoe evie evie ballroom ballroom evie frustum.top.D = -vp(MDRW Boots Waterproof Boots Woman 11Cm Gun And Martin Boots Woman Autumn Bare Shoes Single High Pointed Heel Super Head Short Fine Spring color Heels Boots Heeled Heel ArrqfI1, 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 frustumballroom ballroom evie ballroom shoe evie ballroom evie shoe shoe evie .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0evie ballroom ballroom shoe evie shoe evie shoe evie ballroom ballroom , 2) +shoe shoe ballroom ballroom evie evie evie shoe ballroom ballroom evie vp(3, 2); frustum.right.D = -vp(Buckle 5 Spring Round Women'S Heel Fashion Winter Chunky EU39 Casual Shoes Boots Ankle CN40 Leatherette Toe UK6 Boots US8 Boots Bootie Booties 5 RTRY Wedding For fpqxaFwCp0, 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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