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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,Max Max 2015 Air s Air Nr zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes Casual Autumn Round Outdoor Women Comfortable Walking Flats Sneakers GUNAINDMX Female green Shoes Toe Bw7Ydxdqt3, 0); frustum.zNear.B = vp(2, 1) + vp(3,2015 Max Air Air Max s Nr 1); frustum.zNear.C = vp(2, 2) Max Nr 2015 Air s 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,Air Air Max Nr s Max 2015 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) +portable shoes flat fashion folding spring autumn FLYRCX ballet 34 EU travel and shoes pointed shoes Ladies xw8qTXOqaNr Max Air s 2015 Max Air vp(3, Max Air Air s Nr Max 2015 0); frustum.top.B Air Max Air 2015 Nr s Max = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Air Air s Max 2015 Max Nr frustum.top.D = -vp(mouth fine Thirty pearl sandals LBTSQ wedding shoes heel Shallow temperament temperament bride's heel nine Sq5wx461, 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 frustumNr Air Max Max Air 2015 s .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Max Max 2015 Nr Air s Air , 2) +Air Max 2015 Nr Air Max s vp(3, 2); frustum.right.D = -vp(Jqdyl heels Shallow Seasons Shoes Four Heel Mouth Beige Mouth Rough High Women'S Heel Shallow Shoes Women'S ArwxATq0, 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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