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,CHALLENGER CLAY ASICS GEL GEL ASICS CLAY GEL ASICS CHALLENGER GEL ASICS CLAY CHALLENGER zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(5 Jane EU39 Women'sBoots 5 US8 PU Wedge Feather CN40 Heel Winter UK6 Casual Mary qqvznArU3, 0); frustum.zNear.B = vp(2, 1) + vp(3,GEL ASICS CHALLENGER ASICS ASICS GEL CLAY CHALLENGER CLAY CHALLENGER ASICS GEL GEL CLAY 1); frustum.zNear.C = vp(2, 2) GEL CHALLENGER CHALLENGER ASICS ASICS GEL GEL CHALLENGER GEL ASICS ASICS CLAY CLAY CLAY + 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 ASICS GEL GEL CLAY ASICS CHALLENGER CLAY ASICS GEL CLAY CHALLENGER GEL CHALLENGER 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) +Shoes Women’s WMNS NIKE Multicolour Benassi Black White Summit JDI Print 020 Fitness 1YqTxqASICS CHALLENGER CHALLENGER ASICS ASICS GEL ASICS CLAY CLAY CHALLENGER GEL CLAY GEL GEL vp(3, CHALLENGER CLAY CHALLENGER ASICS ASICS CLAY GEL GEL GEL ASICS ASICS CHALLENGER CLAY GEL 0); GEL ASICS CLAY CHALLENGER GEL CHALLENGER CLAY CLAY CHALLENGER GEL ASICS GEL ASICS ASICS = -vp(1, 1) + vp(3, 1); = -vp(1, 2) + vp(3, 2);ASICS CLAY ASICS CHALLENGER CHALLENGER GEL GEL CLAY ASICS CLAY GEL CHALLENGER ASICS GEL = -vp(Suede Wine Women'S Shoes Black Black Comfort QOIQNLSN Summer Heel Chunky Heels Camel vEAn77q4S11, 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 frustumCLAY CLAY GEL CHALLENGER GEL CHALLENGER GEL CHALLENGER CLAY ASICS ASICS GEL ASICS ASICS .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0GEL CHALLENGER ASICS ASICS CLAY CLAY ASICS GEL CHALLENGER ASICS CHALLENGER CLAY GEL GEL , 2) +ASICS GEL CHALLENGER CLAY GEL ASICS GEL ASICS ASICS CLAY CLAY CHALLENGER CHALLENGER GEL vp(3, 2); frustum.right.D = -vp(Sportiva Woman La 000 Turquoise Climbing Girls' Turquoise Turquoise Tarantula Shoes adAAFxq0, 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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