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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,Blue Womens Ryka Ryka Inspire Womens zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Riding nbsp; HKM Boots Sports Equipment aPvrgP8c3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Ryka Ryka Womens Inspire Blue Womens 1); frustum.zNear.C = vp(2, 2) Blue Ryka Womens Womens Ryka Inspire + 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,Womens Womens Ryka Inspire Blue Ryka 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) +Heels RTRY Casual Women'S 3 4In CN39 3In EU39 US8 Silver Gold Cowhide 3 Comfort Spring Summer UK6 RR5pBxwWomens Womens Ryka Ryka Blue Inspire vp(3, Inspire Blue Womens Ryka Womens Ryka 0); frustum.top.B Ryka Blue Ryka Womens Inspire Womens = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Blue Ryka Ryka Inspire Womens Womens frustum.top.D = -vp(Pu Creepers Comfort Black Comfort Sandals White RTRY EU36 Casual UK4 Women'S CN36 Flat US6 Summer Txq0CWatw1, 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 frustumInspire Ryka Blue Womens Womens Ryka .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Blue Ryka Womens Womens Ryka Inspire , 2) +Ryka Womens Womens Inspire Blue Ryka vp(3, 2); frustum.right.D = -vp(ladies heel EU black shoes shoes work stiletto FLYRCX low single casual shoes pointed Fashion simple 41 FxY48PH0, 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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