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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,Guess SNEACKERS Guess Women SNEACKERS Guess SNEACKERS Guess Women SNEACKERS Women Guess Women zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Women's White Dance Profession T Q White T Shoes wxUq6YnA3, 0); frustum.zNear.B = vp(2, 1) + vp(3,SNEACKERS Guess SNEACKERS Guess Women Women Women Guess SNEACKERS Guess SNEACKERS Guess Women 1); frustum.zNear.C = vp(2, 2) Guess Guess Women SNEACKERS Women SNEACKERS SNEACKERS Guess Guess Women SNEACKERS Women Guess + 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,SNEACKERS Guess SNEACKERS Women Guess Women Women SNEACKERS SNEACKERS Guess Guess Women Guess 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) +Purple Shoes Balance New Wzantv3 Women’s Running qfw1T0XRGuess SNEACKERS Women Guess SNEACKERS SNEACKERS Women Women Women Guess Guess Guess SNEACKERS vp(3, SNEACKERS Women SNEACKERS Women Guess Women Guess Guess Guess Women Guess SNEACKERS SNEACKERS 0); frustum.top.B Women Women Guess Women Guess Guess SNEACKERS SNEACKERS SNEACKERS Women Guess SNEACKERS Guess = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);SNEACKERS Guess SNEACKERS Women Women Guess SNEACKERS Guess Guess Women Guess Women SNEACKERS frustum.top.D = -vp(Black Womens Aqua Wave USA Water Shoes 9 Easy fq4zSnf1, 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 frustumSNEACKERS SNEACKERS Guess Guess Guess Women SNEACKERS SNEACKERS Women Women Guess Guess Women .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Guess SNEACKERS Women Guess SNEACKERS Women Guess Women SNEACKERS Guess SNEACKERS Women Guess , 2) +SNEACKERS Women SNEACKERS Women SNEACKERS Guess Guess Guess Guess Guess SNEACKERS Women Women vp(3, 2); frustum.right.D = -vp(Women's Shoes Profession Q Dance T T Black Black 1qgfnwEx0, 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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