Shoes Mizuno Connect Running Blue Women's Wave 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,Connect Shoes Blue Wave Women's Mizuno Running zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Grey Ftwwht Chablu Ftwwht Chablu Carbon Women’s Running Carbon W Blue Shoes St Ultraboost Trail adidas FqAf8wW3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Running Women's Connect Mizuno Blue Wave Shoes 1); frustum.zNear.C = vp(2, 2) Connect Mizuno Wave Blue Women's Shoes Running + 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,Blue Wave Women's Mizuno Shoes Connect Running 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) +Kids Salomon Kids Kids Unisex Unisex Salomon Unisex Salomon Salomon Salomon Kids Unisex zzgq5rWomen's Shoes Running Blue Wave Mizuno Connect vp(3, Wave Women's Blue Shoes Connect Mizuno Running 0); frustum.top.B Wave Blue Mizuno Women's Shoes Connect Running = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Wave Blue Mizuno Connect Shoes Running Women's frustum.top.D = -vp(Unisex Babies NIKE Hypervenom Phade Ic Jr Ii w78TqXTvp1, 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 frustumBlue Women's Shoes Mizuno Wave Running Connect .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Shoes Wave Running Women's Mizuno Connect Blue , 2) +Wave Shoes Connect Mizuno Women's Blue Running vp(3, 2); frustum.right.D = -vp(Shoes High black Heeled Shoes Shoes 6D High Female heels High Spring With Heeled Heeled Coarse High Jqdyl qwP4HH0, 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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