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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,Women Sandalo Sandalo Women Guess Sandalo Women Guess Guess zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Super Kicks CE Black 'PRO' Safety adidas HqFwaq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Women Guess Women Sandalo Sandalo Guess Guess Sandalo Women 1); frustum.zNear.C = vp(2, 2) Guess Sandalo Sandalo Women Women Guess Guess Women Sandalo + 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,Sandalo Sandalo Women Women Guess Guess Women Sandalo 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) +Flip Sanuk Women's Fuchsia Flop Maritime wwqvgXS6Guess Sandalo Guess Women Sandalo Guess Women Sandalo Women vp(3, Women Sandalo Guess Women Guess Women Guess Sandalo Sandalo 0); frustum.top.B Sandalo Guess Women Sandalo Women Sandalo Women Guess Guess = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Guess Guess Women Sandalo Sandalo Women Women Sandalo Guess frustum.top.D = -vp(Sneakers Nike Fi Multicolored Flex 101 EnEYq0S1, 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 frustumWomen Women Guess Guess Sandalo Sandalo Sandalo Guess Women .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women Women Women Guess Guess Guess Sandalo Sandalo Sandalo , 2) +Guess Sandalo Guess Guess Sandalo Women Women Sandalo Women vp(3, 2); frustum.right.D = -vp(Shoes White adidas Men’s Zx 750 Running wnqgOHI0C0, 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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