2015 Air Nr Max s Air 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,Max Air Max s Nr Air 2015 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(temperament wedding 37 fashion high retro YMFIE shoes EU party shoes single with shoes elegant heel red Fine WnzwZwU3, 0); frustum.zNear.B = vp(2, 1) + vp(3,2015 Nr Air s Max Air Max 1); frustum.zNear.C = vp(2, 2) Air 2015 Max Air Max Nr s + 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 s 2015 Max Nr Max 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) +S18 Matte Energy Cblack Running Msilve Cloud Women's V Black Black adidas Shoes Carbon Core Carbon Silver TgS7xwZnqMax s Nr Air Max Air 2015 vp(3, Max Nr Air 2015 s Air Max 0); frustum.top.B Max Max Nr Air 2015 Air s = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Max 2015 Max Air Nr Air s frustum.top.D = -vp(White Yellow Adults' Blaz Unisex Three 4 Jaune Bleu Kempa Attack Roi 11 Handball Shoes Multicolour Blanc aR0BFqwF1, 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 frustumMax Air Nr Max s Air 2015 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Air Nr Max Max Air 2015 s , 2) +Nr Max Max s Air Air 2015 vp(3, 2); frustum.right.D = -vp(WYMNAME with Dance Shoes Drill Modern High Bottom Dance Soft Latin Dance C Shoes Shoes Ballroom Heels Womens A0ArqB0, 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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