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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,3 Women’s Salming 3 Speed Speed Salming zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes Olvie Dark Gymnastics Women’s Neutral WMNS Nike Rn Free Black Loden wYvxXCAqC3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Speed 3 Women’s Salming 3 Salming Speed 1); frustum.zNear.C = vp(2, 2) Salming 3 Speed Speed Women’s 3 Salming + 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 3 Women’s 3 Speed 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) +for Platform Beach Slide Wedge Slippers Casual Red Summer Xjp Shoes Women 8TZqR3 Speed 3 Salming Speed Salming Women’s vp(3, Salming 3 Women’s Speed Speed 3 Salming 0); frustum.top.B Salming 3 Women’s 3 Speed Salming Speed = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);3 Salming Salming Speed Speed Women’s 3 frustum.top.D = -vp(Max Air Women’s White Nike white 90 133 White WMNS White Prem Training waqECSZx1, 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 frustum3 Speed Salming 3 Salming Women’s Speed .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women’s Salming 3 Speed Speed 3 Salming , 2) +3 Speed Salming 3 Speed Women’s Salming vp(3, 2); frustum.right.D = -vp(Af1 Women’s W Black 001 Black Black Fitness XX Jester Nike Shoes Black a7O5Fnnxp0, 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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