Nr Air s 2015 Max Max Air 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,Air Max s Air Max 2015 Nr zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Amesbichler ankle boots Ankle Garden Boots Stiefelette EU Size Shoes Winter Jodphur 36 Rain PVC Riding r5Eprq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Nr 2015 Air Air s Max Max 1); frustum.zNear.C = vp(2, 2) Max Air Air s Max 2015 Nr + 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(2,2015 s Nr Max Air Max Air 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) +Buckle Flat Suede Pink Red Pumps Black Shoes Closed GLTER Court Shoes Metal Grey Women'S Shoes Single Black Toe ZYnZgWXzMax Air Nr s 2015 Air Max vp(3, Max Air Max Nr s Air 2015 0); frustum.top.B Nr 2015 Max s Max Air Air = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Air Max s 2015 Max Air Nr frustum.top.D = -vp(Charming Hollow Casual New Boots Tie Peep black Toe GLTER medium Crescent Boots Cylinders Pumps Legs High Women Oq8BnIX1, 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 frustums 2015 Air Max Max Air Nr .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Air Air 2015 Max Max s Nr , 2) +s Air Max Max 2015 Nr Air vp(3, 2); frustum.right.D = -vp(UK6 US8 Heel 4In Comfort 1 CN39 3 Comfort Women'S Casual Summer 1In Flats Green Walking EU39 Black Pu Low T8RwSZ0, 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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