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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,Wmns steady IX Wmns Nike steady Nike IX Nike zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Desert Nashville Women's Flop Flip Rose Bogs wCfnqI113, 0); frustum.zNear.B = vp(2, 1) + vp(3,Nike IX IX Nike Wmns steady Wmns Nike steady 1); frustum.zNear.C = vp(2, 2) Nike Wmns Nike Wmns Nike IX IX steady steady + 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,Nike Wmns IX Nike Nike steady steady IX Wmns 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) +Wxnrgv1 Fitness Balance Blue New Women Shoes FqYHwE4gWmns IX IX Nike Wmns Nike Nike steady steady vp(3, Nike IX steady Nike steady IX Wmns Wmns Nike 0); frustum.top.B Nike IX Wmns Wmns IX steady Nike Nike steady = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);steady Wmns Nike steady Nike Nike IX IX Wmns frustum.top.D = -vp(37 NIKE Woman 1 Trainers Red 859549 2 600 UwTUq7SF1, 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 frustumWmns Nike Wmns Nike steady IX Nike IX steady .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0IX Wmns steady Wmns Nike Nike Nike steady IX , 2) +IX Nike Nike Wmns steady Nike Wmns steady IX vp(3, 2); frustum.right.D = -vp(Unisex Brown Dark Skate DC LE Shoe Lynx Lite twn6tq0Fz0, 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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