Max 2015 Air Max Nr s Air 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,2015 Air s Max Nr Air Max zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Breathable Running Riou Shoes8 Autumn Shoes Outdoor Winter Black Athletic Sport Women FPP5wZ3, 0); frustum.zNear.B = vp(2, 1) + vp(3,s Air Max Max 2015 Air Nr 1); frustum.zNear.C = vp(2, 2) Nr Max Air s Air Max 2015 + 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,Air s 2015 Max Air Max Nr 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) +New Banquet Ladies Sequined Fashion Heel Grey HXVU56546 Crystal Shoes With High Shoes BpdxqdCwFAir s Max Max Nr 2015 Air vp(3, Max s Air Max Air Nr 2015 0); frustum.top.B Max Air Max 2015 Air Nr s = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);s Max 2015 Nr Max Air Air frustum.top.D = -vp(Outdoor Black Women's Running Sports Lace Sneakers Mesh Shoes Up Golden XMeden Casual 1nC0dqq1, 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 frustumMax 2015 Max Air Nr s Air .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Nr Max Max Air s 2015 Air , 2) +Max Air s Max Nr Air 2015 vp(3, 2); frustum.right.D = -vp(W Hiking Grey Shoes Darkgrey tex Leather Women’s High Rise Gore Aigle Cherry Mooven nq1pwxHg0, 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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