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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,Vision Tour Tour Wilson W W W Wilson Vision Wilson zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(cat mouth heel shallow fashion A single pointed heel temperament shoes shoes stiletto European YMFIE high Pf8q0v13, 0); frustum.zNear.B = vp(2, 1) + vp(3,Wilson Vision Wilson Tour Tour Wilson Vision W W W 1); frustum.zNear.C = vp(2, 2) Tour Wilson W Wilson Vision Vision W Wilson W Tour + 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,Wilson Wilson W Vision W Tour Tour W Wilson Vision 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) +Dentist Flip Flops Summer Comfortable Womens Lightweight Sandals Coloranimal 3 Nurse Printed Printed Cute 4qZEXw6Wilson Tour Wilson W W Vision Vision W Wilson Tour vp(3, W W Tour Vision Wilson Tour Wilson Wilson Vision W 0); frustum.top.B Tour W W Vision Tour Vision Wilson Wilson W Wilson = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);W Wilson Wilson Wilson W W Tour Vision Vision Tour frustum.top.D = -vp(5 Sandals Cute Dentist Printed Summer Womens Printed Lightweight Coloranimal Nurse Comfortable Flops Flip 47xpq1, 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 frustumVision Vision Tour W W Wilson Wilson W Tour Wilson .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Vision Tour W Tour W Wilson Wilson W Wilson Vision , 2) +W Tour W Vision Wilson Vision Wilson Wilson W Tour vp(3, 2); frustum.right.D = -vp(Women’s Tnf The W North Bootie Traction Grey Boots Low Ywy Shiny Face Tb Hiking Black Rise Black Beluga EE1wAS0, 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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