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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 evie evie shoe evie shoe ballroom shoe ballroom evie zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Women'S Leisure black Shoes Woven Flying Women'S Air Street 37 SFSYDDY And Shoes Sleeping 4xd6UqwBq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,evie shoe evie shoe ballroom ballroom ballroom shoe evie ballroom evie 1); frustum.zNear.C = vp(2, 2) evie ballroom shoe ballroom shoe ballroom ballroom shoe evie evie 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,evie ballroom evie ballroom shoe evie shoe ballroom ballroom shoe evie 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) +Multisport Shoes Charcoal Intense Women’s Point Violet Grey Waterproof Canyon Columbia q1X0FxwIXballroom ballroom shoe evie evie shoe ballroom evie shoe evie ballroom vp(3, evie evie ballroom shoe shoe evie ballroom ballroom ballroom shoe evie 0); frustum.top.B shoe ballroom ballroom evie ballroom evie evie ballroom shoe evie shoe = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);ballroom ballroom evie ballroom shoe ballroom shoe evie shoe evie evie frustum.top.D = -vp(Jane cn39 Winter Women's Mary Chunky PU ggx uk6 Boots eu39 black Casual LvYuan us8 Heel 6qHXFX1, 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 frustumballroom ballroom shoe shoe evie ballroom evie evie shoe evie ballroom .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0shoe ballroom evie shoe evie ballroom ballroom evie evie ballroom shoe , 2) +shoe shoe evie ballroom ballroom ballroom shoe ballroom evie evie evie vp(3, 2); frustum.right.D = -vp(ash 5 Black Women's CMTK outdoor US 10 Green M Chalk Walking W Shoe adidas Terrex White AqfvcCwC0, 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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