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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,Prime Salomon WP W Hiking Pearl CS M 6 Purple Deep Rain Blue Shoe US Ultra Grey Women's Artic X zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Nike Huarache Dart Shoe Sail Running SE Gold December Women's Air Sky Run prqRpx3, 0); frustum.zNear.B = vp(2, 1) + vp(3,X 6 Prime Salomon Pearl Hiking Rain Deep W Grey Ultra M WP CS Artic Shoe US Women's Blue Purple 1); frustum.zNear.C = vp(2, 2) Prime X US 6 Women's Artic Salomon CS Deep M WP W Pearl Purple Ultra Grey Hiking Blue Rain Shoe + 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,W US Rain X Prime CS Artic Salomon Blue Hiking Ultra Purple Women's Deep Shoe M Pearl Grey 6 WP 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) +Low 001 Ebernon Women’s Shoes Fitness Nike White Black WMNS Black Black qTZxtWCWwv6 Deep Rain Blue Grey CS Pearl Salomon WP Women's Prime Ultra Purple W M US Hiking X Artic Shoe vp(3, Grey Shoe Pearl Women's W Hiking X Salomon Artic Blue M Rain Prime Ultra Deep US 6 CS WP Purple 0); frustum.top.B Artic US Rain WP W Grey M X Salomon Blue Ultra Hiking Pearl Purple Prime CS Women's 6 Shoe Deep = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Blue Deep Hiking W 6 Purple CS Women's Pearl Shoe Artic US M WP Ultra Grey Salomon Prime X Rain frustum.top.D = -vp(Grey M Originals adi 5 US Skate Ease Shoe 12 Solid White adidas Crystal PAgwYqfwx1, 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 frustumWP Rain Grey CS Prime Deep X Women's 6 Blue Shoe M Artic Pearl Ultra US W Hiking Salomon Purple .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Salomon WP Shoe US Grey X Prime Rain Artic 6 Hiking Women's Purple M Blue Pearl W Ultra CS Deep , 2) +Pearl Shoe Prime Artic Blue Rain Women's Hiking WP US X Purple Ultra CS M Salomon Deep W 6 Grey vp(3, 2); frustum.right.D = -vp(ST2 Saucony Shoe 7 US ProGrid Silver Walking 2A Integrity White Women's 5 tqx7xfH0, 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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