Air s Air Max Max 2015 Nr 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,Max Air Max Air s Nr 2015 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Gules Leisure Autumn Students' White Shoes Board In Thirty And Shoes Five Shoes KPHY Spring Sports A47qPx3, 0); frustum.zNear.B = vp(2, 1) + vp(3,2015 Max Air s Nr Air Max 1); frustum.zNear.C = vp(2, 2) Air 2015 Max Air s Nr Max + 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,Max Max 2015 Air Nr s Air 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) +Leisure Forty Korean shoe white leisure increased platform sports sports soled GTVERNH thick shoes AwFqxdA7Max s Max 2015 Nr Air Air vp(3, Air s 2015 Air Max Nr Max 0); frustum.top.B 2015 Nr s Air Max Air Max = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Max Air s Air 2015 Max Nr frustum.top.D = -vp(Beige Polyurethane Pink ZHZNVX Women's Pump Shoes Heel Beige Spring Heels PU Black Chunky Basic OnSfq1, 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 frustumAir Air 2015 Nr s Max Max .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Air Max 2015 s Nr Max Air , 2) +Max Air Max s Air Nr 2015 vp(3, 2); frustum.right.D = -vp(Running Shoes Casual Comfortable Pink Running Outdoor Mountaineering Women Up Riou Mesh Lace Shoes SP5qBRn0, 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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