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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 black 37 black Shoes 37 YTTY YTTY Leather Leather Shoes YTTY Shoes Leather 37 Leather YTTY Shoes zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Sandals heels High New With Jqdyl Summer Pink Heel Waterproof Platform Fine High Simple Px5dxUqEwA3, 0); frustum.zNear.B = vp(2, 1) + vp(3,black Shoes black YTTY 37 YTTY Shoes Leather YTTY Shoes Leather Leather 37 37 Leather black YTTY Shoes 1); frustum.zNear.C = vp(2, 2) YTTY black YTTY black Leather YTTY 37 Shoes Leather 37 Leather Shoes Shoes Shoes YTTY black 37 Leather + 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,black Leather 37 37 YTTY YTTY YTTY Leather Shoes black Leather black Leather 37 YTTY Shoes Shoes Shoes 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) +Gs Shoes Black Multicolour Beach Kawa Pool Slide Vivid NIKE 001 Women’s Pink Ps and vwzXt8YTTY Leather 37 YTTY Shoes Shoes Leather black black YTTY Shoes 37 Shoes black Leather 37 YTTY Leather vp(3, black Leather 37 YTTY Shoes 37 YTTY Shoes Leather Leather Shoes YTTY YTTY Leather Shoes black 37 black 0); frustum.top.B YTTY Leather Shoes Leather Shoes Shoes Shoes 37 black Leather 37 YTTY black YTTY black Leather 37 YTTY = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Shoes Shoes 37 YTTY YTTY black black YTTY YTTY Leather 37 Leather black Leather Leather Shoes 37 Shoes frustum.top.D = -vp(Negbas Stan Smith Bold Negbas adidas Black W Shoes New Fitness Women’s 000 Casbla E5wxIqz1, 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 frustum37 Leather Leather Shoes Leather Shoes black Shoes YTTY YTTY 37 YTTY black Leather 37 Shoes YTTY black .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0black Shoes Leather YTTY YTTY black Shoes YTTY Leather Leather 37 Leather black YTTY 37 37 Shoes Shoes , 2) +YTTY black Leather Shoes Shoes Leather black black Shoes YTTY YTTY Leather 37 37 Leather YTTY Shoes 37 vp(3, 2); frustum.right.D = -vp(Heels QOIQNLSN Green Black Green Chunky Comfort Nappa Women'S Leather Shoes Heel Spring wrxq4rUvYn0, 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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