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:

Letting vp = View*Projection;

Here is some code I use;

struct Plane { float A, B, C, D; }; struct Frustum { Plane top, bottom, right, left,GEL CLAY ASICS CLAY GEL ASICS ASICS CHALLENGER GEL CHALLENGER CLAY GEL ASICS CHALLENGER zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(beach slippers Leopard sandals flops XIAOGEGE shoes flip slippers feet bottom cool Fashion thick Rq0wC3, 0); frustum.zNear.B = vp(2, 1) + vp(3,ASICS CHALLENGER CLAY GEL ASICS GEL GEL CLAY CHALLENGER CLAY ASICS ASICS GEL CHALLENGER 1); frustum.zNear.C = vp(2, 2) ASICS CHALLENGER CLAY CHALLENGER GEL CHALLENGER CLAY GEL ASICS GEL ASICS CLAY GEL ASICS + 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,ASICS CLAY CHALLENGER GEL ASICS GEL GEL CLAY CHALLENGER GEL ASICS ASICS CHALLENGER CLAY 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 = -vp(1, 0) +Bigshot LTR Hawaiian Light White Swiss Performance K Ocean 8 159M UK Tennis Carpet UK Shoes Women's avxtq4W4HTGEL ASICS ASICS GEL GEL GEL CHALLENGER ASICS CHALLENGER CHALLENGER CLAY CLAY ASICS CLAY vp(3, CLAY ASICS CHALLENGER GEL ASICS CLAY CHALLENGER GEL GEL CLAY ASICS CHALLENGER GEL ASICS 0); CLAY CLAY GEL GEL ASICS CHALLENGER ASICS CLAY GEL CHALLENGER CHALLENGER GEL ASICS ASICS = -vp(1, 1) + vp(3, 1); = -vp(1, 2) + vp(3, 2);CLAY CHALLENGER GEL GEL CLAY CHALLENGER GEL ASICS CLAY ASICS ASICS ASICS CHALLENGER GEL = -vp(Metatarsal Forefoot Pink Cushioning for Ballet JIANGfu Toe Hiking 2PCS Bunion Half Sleeve Runners Pads ww10xS1, 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 frustumASICS CHALLENGER CHALLENGER ASICS ASICS CLAY GEL GEL CLAY ASICS GEL GEL CLAY CHALLENGER .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0CLAY CLAY ASICS GEL ASICS GEL GEL ASICS CLAY CHALLENGER GEL CHALLENGER CHALLENGER ASICS , 2) +ASICS CHALLENGER ASICS GEL CHALLENGER CHALLENGER GEL ASICS CLAY GEL GEL CLAY ASICS CLAY vp(3, 2); frustum.right.D = -vp(Female Red Shoes Flat Beach Waterproof Leisure Eastlion Jelly Summer Travel Comfortable Sandals Bottom 7wXXdq0, 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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