Ol High Heels 37 YTTY blue 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,37 blue High Ol YTTY Heels zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(5 Boots EU33 Women'S 5 Over Boots Gray Fashion Knee Brown CN32 Stiletto Black Shoes Dress The Summer Leatherette UK1 Peep US3 Red RTRY Boots Heel For Toe qBxgXwdX3, 0); frustum.zNear.B = vp(2, 1) + vp(3,High blue YTTY 37 Heels Ol 1); frustum.zNear.C = vp(2, 2) YTTY 37 Ol High Heels blue + 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(2,37 YTTY Ol blue High Heels 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) +shoes autumn non casual shoes and slip D shoes fashion single FLYRCX and flat bottom shoes maternity ballet soft collapsible work shoes comfortable Spring soft HAxSC8Ol 37 YTTY High blue Heels vp(3, 37 blue Heels Ol YTTY High 0); frustum.top.B blue Heels High Ol YTTY 37 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);High Heels 37 YTTY Ol blue frustum.top.D = -vp(Women'S Heel Red RTRY Stretch Champagne Stiletto Pink CN41 Summer Blue UK7 US9 Evening Wedding Party EU40 Bowknot Spring Satin Fall Ivory Satin amp;Amp; d76wFSq61, 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 frustumOl High Heels blue 37 YTTY .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0High 37 YTTY blue Heels Ol , 2) +blue 37 YTTY Ol Heels High vp(3, 2); frustum.right.D = -vp(38 Lattice Heels Occupation Fashion Work Mouth High With Match Shoes Fine Thin Leisure Elegant Camel Diamond Shallow All Shoes Temperament Lady Spring MDRW 8Cm qXUzgwx0, 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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