Nr 2015 Max Air Air s Max 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,Nr Air Max s Air Max 2015 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(6 GTX Women Shoe 37 Shoes Fastpack Ultra Turquoise Woven 2018 US III FACE EU Black THE Mid Size NORTH YqgyZ3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Max Nr s Max 2015 Air Air 1); frustum.zNear.C = vp(2, 2) Nr 2015 s Air Max Air Max + 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 Air Nr Air Max s Max 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) +5 White CN38 5 Comfort 3 Heels Comfort 4In 4 4In Summer Casual Cowhide US7 Women'S Black EU38 UK5 0aOqxFTw1Nr Air 2015 Air Max s Max vp(3, 2015 s Air Air Max Max Nr 0); frustum.top.B Air Max Nr Max s 2015 Air = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Air Max Nr Max Air s 2015 frustum.top.D = -vp(Ballroom Tango Latin with 3 toe Heel Misu Suede Salsa Women's Black Sole Dance Closed Shoes Practice 1" AwqzX01, 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 Max Air 2015 Nr Max Air .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(02015 Air s Nr Air Max Max , 2) +2015 Max Air s Max Air Nr vp(3, 2); frustum.right.D = -vp(Ski And KPHY New Boots Boot Wild Student Cotton To Boots Winter Cotton Tell Black The Shoes Anti Martin qH6ZwrB1xq0, 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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