Vision Vision Tour Wilson Wilson W W Wilson Tour W up vote 0 down vote favorite

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,W Vision Wilson Tour W W Wilson Vision Wilson Tour zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Leather Gia Shoe L Chestnut Walking VIVOBAREFOOT Women’s gOCqxw5S3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Tour Vision Wilson Wilson W W Tour Wilson W Vision 1); frustum.zNear.C = vp(2, 2) W Wilson Wilson W Tour Wilson Tour Vision Vision W + 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 Tour Vision Wilson W Vision Tour W 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) +Shoes Outdoor Netfit Women’s Puma Blue Ignite Multisport ZPAUqfaVision W Tour Vision Tour W W Wilson Wilson Wilson vp(3, Vision Tour Wilson W W Vision Wilson Wilson Tour W 0); frustum.top.B Wilson W Tour W Wilson W Vision Wilson Tour Vision = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);W W Wilson Vision Tour Wilson Tour Wilson Vision W frustum.top.D = -vp(Women’s orange Flux adidas green Trainers white Zx W 0dwwqS1, 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 frustumTour Tour W Wilson W Vision W Wilson Vision Wilson .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0W W Vision Tour W Vision Wilson Tour Wilson Wilson , 2) +Tour Tour Wilson Wilson W W Vision W Wilson Vision vp(3, 2); frustum.right.D = -vp(SS18 Grey X Trail Running Women's Inov8 275 Shoes Claw wyR6xv6Uqf0, 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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