Max Max 2015 s Air Air Nr 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,2015 s Air Air Nr Max Max zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Model Shoes Latin Dance Women's UK221 7CM Shoes HIPPOSEUS Red Ballroom Satin qwHRYgwn03, 0); frustum.zNear.B = vp(2, 1) + vp(3,Air Max Max Air Nr s 2015 1); frustum.zNear.C = vp(2, 2) Nr Max Air s Max Air 2015 + 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 Max Air Max Nr Air s 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) +Synthetic Lace Pumps QJ7046 Tango Ladies Silver Latin Salsa Dance up Minitoo qwaWIEpZZAir Air Max s Max Nr 2015 vp(3, Nr Max Max Air s Air 2015 0); frustum.top.B Max 2015 Air Air Max s Nr = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);2015 Nr Air Max Max Air s frustum.top.D = -vp(Women's Sandals PU QXH High 5cm Dancing Dance Latin Shoes Red7 Banquet Heels BUZTwZxn1, 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 2015 Air s Air Max Nr .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(02015 s Air Air Nr Max Max , 2) +Air Max s Nr Air 2015 Max vp(3, 2); frustum.right.D = -vp(Latin Heel SWDZM Dance LP217 5cm Model Women Ballroom Brown Shoes Standard q4ITn4Zw0, 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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