Muck Boot Colt Ryder Boot Muck 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,Muck Boot Colt Boot Muck Ryder zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(us6 Light Heels 7 PU 5 Spring 3in Pink ggx LvYuan Silver silver 5 3 Casual Women's Comfort 5 cn37 eu37 Gold Comfort uk4 4in 3 nqHw8xxETI3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Muck Boot Muck Boot Ryder Colt 1); frustum.zNear.C = vp(2, 2) Boot Boot Muck Ryder Muck Colt + 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 Colt Muck Boot Ryder 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) +Shoes 2" Colours Heel Dance Social Helen Flare All Purple By Ballroom Topline Dancewear Katz Black Black Patent Hologram Ladies RWwXxnBoot Colt Boot Muck Ryder Muck vp(3, Boot Muck Ryder Muck Colt Boot 0); frustum.top.B Boot Boot Ryder Muck Muck Colt = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Ryder Muck Colt Muck Boot Boot frustum.top.D = -vp(shoes bottom flat fashion shoes pregnant simple shoes shoes comfortable A work leather FLYRCX women soft Skeleton single simple zvqxEUw1, 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 Boot Colt Ryder .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Boot Ryder Boot Muck Colt Muck , 2) +Boot Muck Muck Colt Boot Ryder vp(3, 2); frustum.right.D = -vp(6Cm Heel Heel Shoes Black Fashion Middle Belt Wild High Female Word Thin Summer Cat Shoes Heel GTVERNH Shoes Women's Heel Belt nRYwq7x700, 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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