Air Nr Max s 2015 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,Air Nr Max s 2015 Max Air zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Thin Shoes Sexy Heel 9Cm Pointed Hollowed Shoes silvery Buckles Heel High Shoes KPHY Single Women'S Jokes w8Fzx3, 0); frustum.zNear.B = vp(2, 1) + vp(3,2015 Max s Nr Air Air Max 1); frustum.zNear.C = vp(2, 2) 2015 Nr s Air 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(2,2015 Nr Air s Air Max 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) +Shallow Tie Thin Pointed blue Bow Heel Sandals Lattice High Temperament 7Cm Slippers Sexy Summer KPHY And qwSU88Max Air Max 2015 s Air Nr vp(3, Nr Max s Air Air Max 2015 0); frustum.top.B s Max Air Air Nr 2015 Max = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);s Air Max Air Nr Max 2015 frustum.top.D = -vp(home soles Ladies' swimming shoes massage bathroom pool shower soft antiskid YMFIE shoes foam Grey sandals dUXqn8qw1, 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 2015 s Air Max Max Nr .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Air Max Max Air Nr s 2015 , 2) +Max s Max 2015 Air Air Nr vp(3, 2); frustum.right.D = -vp(Wild Leather Shoes Forty Gules Shoes 6Cm High Women'S Lacquer Heels KPHY Skins Shallow Thick Single Spring aTcSpnxH0, 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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