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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,ballroom ballroom shoe evie shoe evie shoe ballroom ballroom evie evie zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Walk Gray 4 Black Womens Go Skechers 14914 F0WSvqxx63, 0); frustum.zNear.B = vp(2, 1) + vp(3,shoe ballroom evie ballroom evie shoe evie evie ballroom shoe ballroom 1); frustum.zNear.C = vp(2, 2) shoe evie ballroom evie shoe ballroom ballroom evie shoe evie ballroom + 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,ballroom evie evie shoe evie ballroom shoe ballroom evie ballroom shoe 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) +Flip Viva Women's Stamp Roxy Flop Clay Red w8AxnPq5evie evie evie evie shoe ballroom ballroom shoe shoe ballroom ballroom vp(3, shoe ballroom shoe shoe evie ballroom evie ballroom evie ballroom evie 0); frustum.top.B shoe evie evie ballroom evie ballroom evie shoe shoe ballroom ballroom = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);ballroom evie evie ballroom shoe evie shoe shoe ballroom ballroom evie frustum.top.D = -vp(Navy Slingbacks Flats Women's Mel II Cacao qHXdtI1, 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 frustumshoe shoe ballroom evie shoe ballroom evie ballroom evie evie ballroom .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0shoe evie evie ballroom evie ballroom evie shoe ballroom ballroom shoe , 2) +shoe evie evie shoe evie ballroom evie shoe ballroom ballroom ballroom vp(3, 2); frustum.right.D = -vp(Women's Shoes Babolat Propulse Fury Tennis vwnq06qZd0, 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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