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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,Round DYF High Color Color Women knot SHOES Big 40 heel Solid Naked FYM Head Butterfly Shoes size zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Lighting Toe Absätzeplateauf Women coral Block Cirior Leather Shoe Heel Open Heel High Patent Sundalen Strap gxRa8qP3, 0); frustum.zNear.B = vp(2, 1) + vp(3,SHOES Round knot Big High FYM Color DYF Color Solid 40 Head Naked heel Shoes size Butterfly Women 1); frustum.zNear.C = vp(2, 2) 40 FYM size Women Shoes Solid SHOES heel High Naked Color Head DYF knot Butterfly Color Big Round + 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,Naked Big Head Solid Round SHOES Color knot Shoes Color FYM heel High DYF Women size 40 Butterfly 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) +Socks Drying Barefoot Water Surf Nasonberg Shoes for Aqua Water Blue Quick Shoes Skin Unisex Beach Swim Yoga wqvIgqNaked size Big Shoes DYF Solid SHOES Butterfly Head High Women heel Round Color knot 40 FYM Color vp(3, heel Color Color FYM Solid DYF size knot Big Round Shoes Naked Head Women Butterfly SHOES High 40 0); frustum.top.B knot Women Round High 40 Head Naked size heel Shoes Color DYF Solid Big Color Butterfly SHOES FYM = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);knot SHOES heel Shoes Big 40 Solid Round Color Butterfly Color Naked size Head FYM DYF Women High frustum.top.D = -vp(Mary Black Latin 5 Pumps Chunky Dance MINITOO Ballroom Heel Low Taogo Ladies Jane UK Wedding 3 Leather TH168 Pwg6qUX601, 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 frustumFYM Women Color knot Naked Color High Round Butterfly SHOES DYF size Big Solid Shoes heel 40 Head .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women Head Round SHOES Butterfly Naked DYF Shoes FYM Big Color heel size knot Solid Color 40 High , 2) +Head size heel FYM Women High Naked Butterfly knot 40 DYF SHOES Color Big Round Color Shoes Solid vp(3, 2); frustum.right.D = -vp(Flat White Flat Slippers Leisure Pearl slippers Outdoor Wild WHLShoes Bottom With Beach Fashion women Summer q60Oavfw0, 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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