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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,YTTY YTTY 35 Shoes black black Shoes Bullock black YTTY YTTY 35 Bullock Bullock Bullock Shoes 35 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Air Jogging Multi Athletic for Grey Fitness Sport OneMix Pink Running Trainers Shoes Women's nz5nqwaY3, 0); frustum.zNear.B = vp(2, 1) + vp(3,YTTY black Shoes YTTY black 35 black Bullock YTTY YTTY Bullock Shoes 35 35 Bullock Shoes Bullock 1); frustum.zNear.C = vp(2, 2) Bullock Bullock YTTY YTTY 35 YTTY 35 black 35 Shoes black Bullock Shoes Shoes Bullock YTTY 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,black Shoes Shoes 35 35 black Bullock YTTY YTTY Bullock Shoes black 35 YTTY YTTY Bullock Bullock 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) +boots are blue and cotton In thickened barrel women's warm the snow winter embroidery boots 060xawYBqShoes YTTY black 35 Bullock 35 black Bullock YTTY 35 YTTY Shoes Bullock black Shoes YTTY Bullock vp(3, black Bullock YTTY 35 Shoes Shoes Bullock YTTY 35 YTTY Shoes black black 35 Bullock YTTY Bullock 0); frustum.top.B YTTY YTTY Bullock YTTY Bullock Shoes YTTY Bullock 35 35 black Shoes black 35 Shoes black Bullock = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);black YTTY 35 black Shoes Bullock YTTY Shoes black 35 Shoes Bullock Bullock Bullock YTTY YTTY 35 frustum.top.D = -vp(Flat Women Color Nude Shoes Big Bottom Sharp Size 47 Shallow FYM Solid Brown SHOES DYF Mouth fwqxBgv1, 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 frustumShoes YTTY YTTY YTTY black black Shoes 35 Bullock black Bullock Shoes Bullock Bullock 35 35 YTTY .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Bullock black YTTY YTTY YTTY YTTY black 35 Shoes 35 Bullock Bullock Shoes 35 Shoes Bullock black , 2) +Shoes Bullock black Bullock black 35 YTTY Shoes black Bullock 35 35 Shoes YTTY Bullock YTTY YTTY vp(3, 2); frustum.right.D = -vp(Thirty Spring Shoes Autumn And Women'S GTVERNH Increased Shoes Shoes nine Sports New Women'S qXcPwz00, 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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