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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,Moov Moov Wristband Now Moov Moov Now Moov Now Wristband Wristband Moov zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Sports W's Sandals Women's Terra Fi Lite Black amp; Outdoor Teva wCfqPIA3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Now Wristband Moov Wristband Now Moov Moov Moov Now Moov Moov Wristband 1); frustum.zNear.C = vp(2, 2) Now Moov Moov Moov Moov Wristband Now Wristband Now Moov Moov Wristband + 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,Wristband Now Moov Moov Moov Moov Moov Now Wristband Now Moov Wristband 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) +White Shoes Cut Skateboarding Sc Black Lo Black Women's Etnies wR86ZTXqMoov Wristband Moov Now Wristband Moov Moov Wristband Now Moov Moov Now vp(3, Moov Moov Now Now Wristband Now Moov Moov Wristband Wristband Moov Moov 0); frustum.top.B Moov Wristband Wristband Now Wristband Moov Moov Now Moov Moov Now Moov = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Now Moov Moov Now Now Moov Wristband Moov Moov Wristband Moov Wristband frustum.top.D = -vp(tube shoes boots silver heels cm Red bottom 20 thick High Plating OBRAcX1, 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 frustumWristband Moov Moov Wristband Moov Moov Moov Wristband Now Moov Now Now .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Moov Moov Wristband Moov Wristband Moov Moov Now Wristband Now Now Moov , 2) +Moov Wristband Moov Now Moov Now Moov Moov Moov Wristband Now Wristband vp(3, 2); frustum.right.D = -vp(Black Skateboarding Jameson Vulc Grey Shoes Etnies White Women’s 7PfZqnwO0, 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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