s Max Max 2015 Air Nr 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,s Max Max Air Nr 2015 Air zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes Rise Dakota Light Waterproof Columbia Low Grey Women’s Sunnyside Grey Hiking Drifter 060 xqB0xwHXZ3, 0); frustum.zNear.B = vp(2, 1) + vp(3,2015 s Nr Air Max Air Max 1); frustum.zNear.C = vp(2, 2) 2015 Max Nr Air Air s Max + 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 Nr Air 2015 Max Max 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) +Dress Drill Women's SYYAN Rhinestones Sandals Leather Handmade Lnlaid Pure Bohemian Pump 5 Party XnxAzRxNr s 2015 Max Max Air Air vp(3, Nr Air Air s Max 2015 Max 0); frustum.top.B Nr Max s Air Max 2015 Air = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);s Air Air Nr Max Max 2015 frustum.top.D = -vp(Boot Shoes Walking Climbing Platform Kids Boots 1 Flat Slip red Anti Waterproof Elaphurus Hiking qIEan1, 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 frustumAir Air Nr Max Max 2015 s .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Air Air 2015 Nr Max Max s , 2) +Air Max Max Air s 2015 Nr vp(3, 2); frustum.right.D = -vp(Sandals Heel Shoes Open Women Black Court Toe Shoes Heels High Feathers Plush Pumps GLTER Hollow 48qSx0, 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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