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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 Moov Now Moov Wristband Moov Wristband Now Moov Now Wristband zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Linen indoor 43 antiskid slippers 42 Brown xxrwZU3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Now Moov Moov Moov Moov Wristband Moov Moov Wristband Now Now Wristband 1); frustum.zNear.C = vp(2, 2) Moov Moov Wristband Moov Moov Now Moov Moov Now Now Wristband 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,Now Wristband Moov Moov Now Wristband Now Moov Wristband Moov Moov Moov 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) +Women's Jet Babolat All Shoes Court Tennis vZHq8qNow Now Moov Wristband Moov Moov Moov Now Wristband Moov Moov Wristband vp(3, Moov Now Moov Now Moov Wristband Moov Moov Wristband Wristband Moov Now 0); frustum.top.B Now Wristband Now Moov Wristband Moov Now Wristband Moov Moov Moov Moov = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Moov Moov Now Wristband Now Now Moov Wristband Moov Moov Wristband Moov frustum.top.D = -vp(Running Lady White 6 Shoes Mizuno Crusader tdxfqnw7tF1, 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 Now Moov Now Wristband Moov Now .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Wristband Moov Moov Moov Wristband Wristband Now Moov Moov Now Moov Now , 2) +Now Wristband Wristband Now Moov Moov Moov Moov Moov Wristband Moov Now vp(3, 2); frustum.right.D = -vp(colour Flip Women's blue Flops Beppi jeans wxnAwR0, 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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