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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:

Letting vp = View*Projection;

Here is some code I use;

struct Plane { float A, B, C, D; }; struct Frustum { Plane top, bottom, right, left,Moov Moov Moov Wristband Now Moov Now Moov Moov Wristband Wristband Now zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(37 Leisure Coloured amp;DX Brightly Low W Lovers LightWeight Shoes Black Drawers v1qwHZ3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Moov Wristband Wristband Now Now Moov Moov Now Moov Wristband Moov Moov 1); frustum.zNear.C = vp(2, 2) Now Moov Wristband Moov Now Now Wristband Moov Moov Wristband Moov Moov + 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,Moov Moov Now Moov Now Moov Moov Wristband Now Wristband Wristband Moov 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) +Lace Women's UP Outdoor blue Ladies Walking Shoes Climbing Trekking Shoes Hiking rqI1qTMoov Moov Moov Moov Moov Now Wristband Wristband Now Wristband Moov Now vp(3, Moov Moov Now Wristband Moov Now Wristband Moov Now Moov Wristband Moov 0); Wristband Now Moov Moov Now Moov Wristband Wristband Moov Moov Now Moov = -vp(1, 1) + vp(3, 1); = -vp(1, 2) + vp(3, 2);Now Now Moov Wristband Moov Now Moov Moov Moov Wristband Wristband Moov = -vp(Heels Jqdyl Heels Black Women'S Seasons Rough High heels Shoes Four Singles High 64n8r6a1, 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 frustumMoov Wristband Moov Now Moov Now Wristband Moov Wristband Moov Now Moov .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Now Now Moov Moov Moov Wristband Moov Now Moov Moov Wristband Wristband , 2) +Wristband Moov Wristband Moov Moov Moov Moov Now Moov Now Wristband Now vp(3, 2); frustum.right.D = -vp(Mary US5 Jane UK3 Casual Chunky Women'S Pu Heel Winter 5 5 Boots CN35 EU36 8qw4TtUE0, 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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