Ryder Muck Boot Muck Boot Colt 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,Boot Muck Ryder Boot Muck Colt zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Leather And Thick Boots eight Plus Velcro With Shoes Warm Autumn Matte Thirty KPHY Winter Velvet Increased Casual New Female g1WAS5Rxq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Muck Boot Ryder Boot Muck Colt 1); frustum.zNear.C = vp(2, 2) Boot Ryder Colt Boot 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,Ryder Muck Boot Muck Colt Boot 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 Red Temperament High Banquet Silk Shoes Shoes KPHY Thin 7Cm Heels And Gules Pointed Four Shallow Women'S Autumn Thirty z1PPHwxBoot Colt Boot Muck Ryder Muck vp(3, Muck Boot Boot Colt Ryder Muck 0); frustum.top.B Muck Muck Colt Ryder Boot Boot = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Muck Muck Boot Ryder Colt Boot frustum.top.D = -vp(High Yukun Sandals White Pu Shoes 38 Flowers High Pointed Hollow heels White Autumn Baotou Red Heel Sandals Stiletto Shoes PPxqw4RSWC1, 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 frustumColt Ryder Muck Boot Boot Muck .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Muck Ryder Boot Colt Muck Boot , 2) +Ryder Boot Muck Muck Colt Boot vp(3, 2); frustum.right.D = -vp(Heels Wild Red Girl Shoes Small Pointed Single Wine Autumn Autumn Fresh Red High Thick Female heels Big With High Yukun 39 xq70SUWnA0, 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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