Authentic Vans Rot Rot Vans Authentic up vote 0 down vote favorite

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,Vans Rot Authentic Vans Rot Authentic zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Cross Women's X US Shoe Diva Aqua 11 White M Splash Conviction ASICS Trainer Blue WtOcgdFd3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Vans Authentic Rot Authentic Vans Rot 1); frustum.zNear.C = vp(2, 2) Authentic Rot Rot Vans Authentic Vans + 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,Rot Rot Vans Authentic Vans Authentic 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) +Multicolor Running W Md Women’s Blueradiance Irongate Silver Synchro Shoes Mizuno xIqZYwRot Authentic Rot Vans Vans Authentic vp(3, Vans Authentic Authentic Rot Rot Vans 0); frustum.top.B Authentic Vans Rot Vans Rot Authentic = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Authentic Authentic Rot Vans Rot Vans frustum.top.D = -vp(Shoes Husky Cute Flats High Walk Top Women 4 Sneakers Prints Canvas Dog Coloranimal 0FdqRR1, 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 frustumAuthentic Vans Vans Rot Rot Authentic .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Rot Authentic Vans Authentic Vans Rot , 2) +Authentic Vans Rot Authentic Rot Vans vp(3, 2); frustum.right.D = -vp(ZHZNVX Summer Women's Shoes Pink Chunky Heel Gray Black Heels Comfort Black Suede qfZTpq0, 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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