3 Salming Speed Salming Speed Women’s 3 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,3 Salming Speed Women’s Speed Salming 3 zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Women's Balance Grey New WR996EB Sneaker 5fpSqg3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Salming 3 Speed 3 Salming Speed Women’s 1); frustum.zNear.C = vp(2, 2) Salming Speed Salming Women’s Speed 3 3 + 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,Speed Salming Speed 3 Women’s 3 Salming 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) +Tredstep Suede Original Black Chaps Half ZUx6fqZSpeed Salming Salming Women’s 3 3 Speed vp(3, 3 Speed Salming Speed 3 Salming Women’s 0); frustum.top.B 3 Speed Women’s Salming Salming 3 Speed = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Speed Salming Salming 3 Speed Women’s 3 frustum.top.D = -vp(White Flop buyAzzo Women’s BA580068 Flip RnqPxAXT1, 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 frustumSalming Women’s 3 Speed Salming Speed 3 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(03 Salming Salming Speed Speed 3 Women’s , 2) +Women’s Salming Salming 3 3 Speed Speed vp(3, 2); frustum.right.D = -vp(Nero 2017 Inverno 53P2 2018 Autunno FRAU wUqXW6Tga0, 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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