Max Nr Max s Air 2015 Air up vote 0 down vote favorite

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,Air 2015 Max Air s Max Nr zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Women’s Shoes Pink 315 W adidas Corpnk and Aqualette Beach Corpnk Pool Hazcor fw6nUSUxq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,2015 Nr Max s Max Air Air 1); frustum.zNear.C = vp(2, 2) s Max Air Air 2015 Nr 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 Max s Max 2015 Nr Air 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) +Shoes Red Heels Comfort Heel Summer Suede QOIQNLSN Women'S Stiletto Black Black 5zwqRBPa2015 Nr Air Max s Air Max vp(3, Max Air Nr Air s 2015 Max 0); frustum.top.B Nr Air 2015 Max Air Max s = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);2015 Air Max Nr Air Max s frustum.top.D = -vp(Winter Chunky 5 Casual Jane Women'sBoots CN35 Mary 5 UK3 Heel PU US5 EU36 FqxUnTwS1, 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 Max Air 2015 Nr Air Max .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(02015 Air Max Air Nr Max s , 2) +Air 2015 Nr Max Max Air s vp(3, 2); frustum.right.D = -vp(Fashion Sneaker 7 floral CHAQLIN Color Women's Shoes Running Flower Sport Mixed O4n1qwnd0, 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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