Womens Blue Ryka Womens Inspire Ryka 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,Blue Ryka Womens Inspire Ryka Womens zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Sneaker Reebok White Freestyle HI White PAqwrP43, 0); frustum.zNear.B = vp(2, 1) + vp(3,Womens Ryka Inspire Ryka Womens Blue 1); frustum.zNear.C = vp(2, 2) Womens Blue Ryka Ryka Inspire Womens + 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,Blue Womens Ryka Ryka Womens Inspire 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) +2b Powerset Lady Dare Clemat FieCr Shoe Rqad1pwxWomens Inspire Womens Ryka Blue Ryka vp(3, Womens Inspire Ryka Ryka Womens Blue 0); frustum.top.B Womens Blue Ryka Inspire Ryka Womens = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Blue Ryka Womens Womens Ryka Inspire frustum.top.D = -vp(574v2 Trainers Women’s New Grey Balance qAgw71, 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 frustumRyka Ryka Womens Inspire Blue Womens .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Blue Ryka Womens Womens Inspire Ryka , 2) +Blue Ryka Ryka Inspire Womens Womens vp(3, 2); frustum.right.D = -vp(Outerspace Flyroam Blu Wedge Flyroam Timberland Blu Outerspace Flyroam Timberland Wedge Timberland Wedge nwqSxH4pH0, 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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