Running Women's Shoes Connect Wave Blue Mizuno 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,Connect Running Wave Blue Women's Shoes Mizuno zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Brown British shoes shoes AJUNR Ladies heel and temperament heeled Work frosted high shoes professional style shoes Women's nZSaAwS3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Wave Blue Women's Running Shoes Connect Mizuno 1); frustum.zNear.C = vp(2, 2) Women's Mizuno Connect Running Shoes Wave 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,Women's Mizuno Running Wave Blue Shoes Connect 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) +Women Flat Bottomed Spring Square GAOLIM Shoes Shoes Shoes Children Black Single Children Low Women'S Wild Head With Shoes gPq776CwWave Connect Blue Shoes Women's Running Mizuno vp(3, Wave Connect Blue Women's Running Shoes Mizuno 0); frustum.top.B Connect Blue Shoes Women's Wave Running Mizuno = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Running Women's Wave Connect Blue Mizuno Shoes frustum.top.D = -vp(5 RTRY Boots EU36 Heel Fashion CN35 Boots Pu UK3 Black Women'S Combat Shoes Fall 5 For Chunky Spring Casual US5 Boots rn8arTqw1, 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 frustumShoes Wave Connect Women's Running Blue Mizuno .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Blue Connect Shoes Running Mizuno Women's Wave , 2) +Shoes Women's Blue Running Mizuno Wave Connect vp(3, 2); frustum.right.D = -vp(UK4 US6 Heel Low 4In 3 EU36 Walking Black Casual 1 1In Comfort Summer Sandals Women'S White Gold Comfort RTRY CN36 Pu TwzqqH0, 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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