YTTY 37 Ol High Heels blue 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,Heels Ol High YTTY blue 37 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(W Boot Snow Wp Shelter Black Salomon Black Women’s Cs Blue Stone FnqZtHf3, 0); frustum.zNear.B = vp(2, 1) + vp(3,High 37 blue Ol YTTY Heels 1); frustum.zNear.C = vp(2, 2) blue Heels YTTY Ol 37 High + 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,YTTY blue 37 High Heels Ol 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) +Free Nike WMNS Shoes Rn anthracite Gymnastics Black Women’s White xZ4qwExHigh YTTY Ol 37 blue Heels vp(3, Heels Ol blue High YTTY 37 0); frustum.top.B 37 Ol High YTTY Heels blue = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);YTTY High Heels 37 blue Ol frustum.top.D = -vp(Taupe Fly WMNS Grey Running Shoes Competition NIKE Presto Women’s q0ZHzH1, 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 frustumOl Heels blue YTTY 37 High .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(037 High Ol Heels YTTY blue , 2) +Heels Ol 37 High blue YTTY vp(3, 2); frustum.right.D = -vp(Pro GS 700 NIKE Boys Little Volt Posite Shoes black Kids 644792 fw4PBq0, 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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