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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,Muck Muck Ryder Colt Boot Boot zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes Dance Ballroom Bottom Shoes High Latin Dance A Shoes Dancing Soft Shoes Ballroom Ladies Women's GUOSHIJITUAN Heel UqvHx803, 0); frustum.zNear.B = vp(2, 1) + vp(3,Muck Ryder Muck Colt Boot Boot 1); frustum.zNear.C = vp(2, 2) Boot Boot Ryder Colt Muck Muck + 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,Boot Ryder Muck Boot Colt Muck 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) +Nondye White Terrex Cwhite Speed 6 Agravic 5 UK Nondye Ftwwht Shoes Women’s Trail Running adidas Ftwwht Grey Cwhite 17nfPfBoot Muck Muck Boot Colt Ryder vp(3, Boot Ryder Colt Boot Muck Muck 0); frustum.top.B Muck Boot Colt Muck Boot Ryder = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Colt Muck Ryder Boot Boot Muck frustum.top.D = -vp(Gridiron 35 Dark Zoom Purple Women’s Air Multicolored Provence Competition NIKE Pegasus Running Shoes Citron 500 WMNS Xxg4qnwA61, 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 frustumMuck Boot Muck Colt Boot Ryder .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Boot Colt Muck Ryder Muck Boot , 2) +Ryder Boot Colt Muck Boot Muck vp(3, 2); frustum.right.D = -vp(Nike Cool Grey Wolf Rn Free Women’s Running 2 Grey White Black Women's Multisport Indoor Distance Shoes Stealth Grey rPqrC0, 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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