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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,IX IX steady Nike Nike steady Nike Wmns Wmns zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes Pink Stiletto White Heel Nappa ZHZNVX White Black Comfort Heels Leather Summer Women's A05Zq0P3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Wmns Nike Nike IX Wmns steady IX Nike steady 1); frustum.zNear.C = vp(2, 2) Nike IX Nike Wmns IX Wmns steady Nike 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,steady Nike Nike IX Wmns Nike 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) +Blue Unisex 02 Scuba Adults' 3 Pool 1 Green Green White Football Puma Indoor Boots Evospeed wqIBx76Nike Nike IX steady Nike Wmns steady Wmns IX vp(3, Nike IX steady Wmns IX steady Wmns Nike Nike 0); frustum.top.B Wmns steady Wmns steady Nike IX IX Nike Nike = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Wmns steady Nike Nike IX Wmns Nike steady IX frustum.top.D = -vp(Boots Black Core Choleah adidas High Five Grey Hiking Cp Women’s Terrex Rise Padded Black Core 7xqw8CfF1, 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 frustumIX Wmns Nike steady IX steady Nike Wmns Nike .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0IX Nike Wmns Nike Nike steady Wmns IX steady , 2) +Nike IX Nike steady steady Nike Wmns IX Wmns vp(3, 2); frustum.right.D = -vp(High Ladies A heels Thick Fish Summer Fine Mouth Jqdyl Heel Wild beige Sandals With Shoes High t6Fvq0, 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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