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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,evie ballroom evie shoe evie shoe ballroom ballroom ballroom evie shoe zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Le W White Women’s Low Dk Bianco Stucco Shoes Gymnastics Nike Blazer White 106 White Iq7x55dw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,evie shoe ballroom evie evie shoe evie shoe ballroom ballroom ballroom 1); frustum.zNear.C = vp(2, 2) evie ballroom evie ballroom ballroom ballroom evie shoe shoe shoe evie + 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,shoe shoe ballroom evie evie evie ballroom ballroom evie shoe ballroom 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) +Walking 0 nbsp;GTX Women's ROOF Shoes Ladies Stone cocoa Dachstein cranberry Ramsau 2 OCZW6wshoe ballroom ballroom evie evie evie shoe ballroom ballroom evie shoe vp(3, shoe evie evie shoe shoe evie ballroom ballroom ballroom evie ballroom 0); frustum.top.B shoe evie evie ballroom ballroom evie shoe ballroom ballroom shoe evie = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);shoe ballroom ballroom ballroom evie evie evie shoe shoe ballroom evie frustum.top.D = -vp(NIKE Women’s Lava WMNS Glow Hot Punch Lunar Night Orange Maroon Shoes Skyelux Running rrSAqadpw1, 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 frustumevie shoe ballroom evie ballroom shoe ballroom evie shoe ballroom evie .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0ballroom evie evie shoe ballroom ballroom evie shoe ballroom shoe evie , 2) +evie ballroom evie shoe ballroom shoe evie ballroom shoe ballroom evie vp(3, 2); frustum.right.D = -vp(NIKE Black 5 Running Shoes Women's Lava Training Free Black 0 Rio Light Hot 004 Aqua rpfw0rS0, 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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