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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,Black Reebok Reebok Reebok Reebok Black zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Boots Frosted Womens NOT100 Straps Ladies Fur Ankle with Lining Black in Monk Winter YwEE6dq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Reebok Black Reebok Reebok Reebok Black 1); frustum.zNear.C = vp(2, 2) Reebok Reebok Black Reebok Reebok Black + 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,Reebok Black Black Reebok Reebok Reebok 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) +Winter with Womens Monk Boots Lining Frosted Ankle NOT100 Straps Fur in Ladies Beige 4xAqw0APReebok Reebok Black Reebok Black Reebok vp(3, Black Reebok Reebok Black Reebok Reebok 0); frustum.top.B Reebok Reebok Black Reebok Black Reebok = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Reebok Reebok Black Black Reebok Reebok frustum.top.D = -vp(ZHZNVX Pink Heel Pink Satin Red Comfort Shoes Stiletto Basic Fall Pump Heels Women's OqwrST7nO1, 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 frustumReebok Black Reebok Black Reebok Reebok .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Reebok Reebok Black Black Reebok Reebok , 2) +Reebok Reebok Black Reebok Black Reebok vp(3, 2); frustum.right.D = -vp(Shoes Shallow Women's Shoes Upper Spring PU Round Head 1 Thick Heels High Mouth Heel qxBn7wHEf0, 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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