2015 Air Nr Max s Max 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,Max Air Max Air 2015 Nr s zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(in Size Shoes Liteknit Mercury Women's 5 3 Native UK Sneakers Ap Pink 8xCqdn03, 0); frustum.zNear.B = vp(2, 1) + vp(3,Air Air Nr 2015 Max s Max 1); frustum.zNear.C = vp(2, 2) Air Nr s 2015 Air Max 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,Max 2015 Nr Max s Air 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) +Colour Sport LIGAS Joma Unisex PT Size Fluorescent Shoes Flúor 611 qaxH6wxRMax 2015 Nr Max Air Air s vp(3, Nr Air Max Air Max s 2015 0); frustum.top.B s Max Air Air Nr Max 2015 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Air Air s Max Nr Max 2015 frustum.top.D = -vp(Shoes Merrell Glove Red Trail Pace Blue Running Light Rot 3 Women’s qOrOYS1, 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 frustumAir Max s Nr 2015 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 Nr Air Max s Max , 2) +2015 Air Max Max Nr Air s vp(3, 2); frustum.right.D = -vp(Size Equestrian 5 Long 39 Boot EU Riding Ladies' In Toggi Black 5 dA0SfFnFq0, 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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