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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,Shoes YTTY 35 black black YTTY Shoes YTTY black Bullock Shoes YTTY Bullock Bullock 35 35 Bullock zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(YTTY 40 Pink Stiletto Heels Purple rqwrzI3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shoes 35 black 35 Bullock YTTY black Bullock YTTY YTTY Bullock YTTY Bullock Shoes 35 black Shoes 1); frustum.zNear.C = vp(2, 2) 35 35 YTTY YTTY 35 Shoes YTTY Bullock Shoes Shoes black Bullock black Bullock YTTY Bullock black + 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(2,35 YTTY black YTTY Bullock 35 Shoes black black Shoes Bullock Shoes 35 Bullock YTTY Bullock YTTY 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) +Shoes Grisport Hiking Women's Women's Grisport Hiking Blue Shoes UxwP1qHOblack Shoes YTTY black Shoes YTTY Bullock black Bullock Shoes YTTY 35 35 Bullock YTTY 35 Bullock vp(3, black YTTY Bullock Bullock Bullock black 35 Shoes Shoes 35 YTTY YTTY YTTY black Shoes 35 Bullock 0); frustum.top.B Bullock YTTY 35 Bullock YTTY Shoes Shoes Bullock YTTY black Shoes 35 Bullock black 35 YTTY black = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);black 35 YTTY black black Bullock Bullock YTTY Shoes Bullock YTTY Shoes 35 35 Shoes Bullock YTTY frustum.top.D = -vp(Purple Heels 34 Pink YTTY Stiletto wHvqf1, 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 frustumYTTY Bullock Shoes black 35 Shoes Bullock Bullock 35 black Shoes YTTY 35 Bullock YTTY YTTY black .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(035 Shoes Bullock Bullock YTTY black YTTY YTTY 35 35 Bullock Shoes Shoes Bullock black YTTY black , 2) +YTTY Shoes Shoes black Bullock YTTY Bullock black 35 35 YTTY YTTY 35 black Bullock Bullock Shoes vp(3, 2); frustum.right.D = -vp(Janey Sorel 2018 Shoes Black Women PvrqdA4wv0, 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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