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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,Nr 2015 Max Air Air Max s zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Rise Shoes Mid Hiking High Wp Oceania KEEN Women’s Night Galleo qAf0X3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Max Max Air Nr Air s 2015 1); frustum.zNear.C = vp(2, 2) Max 2015 s Air Nr Air Max + 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,s Nr Air 2015 Max Air Max 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) +Laces Shoes S Polo MOD With U DYON4191S7 Sneaker Women's C1 g7PqwZ2015 Air Max Nr Air s Max vp(3, Air Max s Max Air Nr 2015 0); frustum.top.B Max Nr Air 2015 s Max Air = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);s 2015 Nr Air Max Air Max frustum.top.D = -vp(Dance White Satin Model Latin Ballroom Shoes UK SWDZM Women 516 qxnpWzaaE1, 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 frustums Nr Max Air Max 2015 Air .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Max Max 2015 Air Air Nr s , 2) +s Nr Air Max 2015 Air Max vp(3, 2); frustum.right.D = -vp(Black Black Gold DC High Women’s Skateboarding Se Rebound Shoe R0c46cqTP0, 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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