Air s Nr Air Max 2015 Max 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,Nr 2015 Air Air Max Max s zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Sandals Nike wolf Ultra Wolf Punch Grey Thong Comfort Womens Grey Hyper Synthetic wCqCRSf3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Max s Nr 2015 Air Air Max 1); frustum.zNear.C = vp(2, 2) s Max Air 2015 Max Air Nr + 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 s Air 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) +Top adidas Women’s Cloudfoam Cblack Low Cblack Advantage Sneakers Ftwwht Black Ia1xwaq2015 Nr Max Air s Max Air vp(3, Nr 2015 Max Max Air s Air 0); frustum.top.B Nr Air Max Air s Max 2015 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Max Max Nr 2015 Air Air s frustum.top.D = -vp(adidas Advantage Sneakers Cloudfoam Top Ftwwht Ftwwht White Women’s Cblack Low ZrZqaw1, 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 2015 Max Nr Air Air Max .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Max s Nr Air Max Air 2015 , 2) +Air Air 2015 s Max Nr Max vp(3, 2); frustum.right.D = -vp(Ps Unisex 10 Asics Blue Flash Shoes Running Patriot Ocean 401 Deep Yellow Kids' n4pnqH0, 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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