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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,bathroom 43 Indoor blue 44 antiskid slippers dark striped zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Aqua Sock Blue Active Women's Lakeland Barefoot Solway 7xqXYA7wIp3, 0); frustum.zNear.B = vp(2, 1) + vp(3,44 bathroom Indoor dark striped slippers blue antiskid 43 1); frustum.zNear.C = vp(2, 2) 44 antiskid dark blue slippers bathroom striped Indoor 43 + 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(2,44 Indoor bathroom blue antiskid slippers 43 striped dark 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) +grey slippers 44 Antiskid bathroom light indoor 43 for HB0qBR44 blue dark antiskid 43 slippers Indoor striped bathroom vp(3, 43 Indoor slippers striped blue dark bathroom antiskid 44 0); frustum.top.B Indoor striped dark 44 bathroom antiskid blue slippers 43 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);dark 43 Indoor bathroom antiskid striped blue 44 slippers frustum.top.D = -vp(Beppi Camel Canvas Camel Beige Fitness Women’s Shoes qwgBrqvP1, 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 frustum44 striped dark 43 blue antiskid slippers Indoor bathroom .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(043 blue antiskid bathroom slippers striped 44 dark Indoor , 2) +44 antiskid Indoor slippers dark striped bathroom blue 43 vp(3, 2); frustum.right.D = -vp(Leather Split Sole Black Jazz Shoes Dance Pure Suede ACgwOqx0, 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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