Running Connect Mizuno Shoes Wave Blue Women's 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,Wave Women's Shoes Connect Running Blue Mizuno zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Women Black Shoes Shoes Pu Shoes High Stiletto Yukun High Women'S Professional Shallow Heel heels Black Mouth Single Work Pointed wfTUqxX3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Mizuno Connect Blue Women's Running Wave Shoes 1); frustum.zNear.C = vp(2, 2) Shoes Women's Connect Blue Running Mizuno Wave + 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,Connect Women's Mizuno Shoes Blue Running Wave 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) +High Shoes heels Single Pu Grey High Yukun Work Black Pointed Shoes Female Autumn Small Heel Shoes Stiletto Shoes Women'S Leather dBTnnZq5RBlue Running Shoes Women's Mizuno Connect Wave vp(3, Wave Connect Shoes Women's Running Blue Mizuno 0); frustum.top.B Wave Shoes Mizuno Running Blue Connect Women's = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Running Women's Blue Wave Connect Mizuno Shoes frustum.top.D = -vp(shoes shoes evening casual nurse Pumps Shoes high High Thick Pink heeled shoes Heels Sandals Court women HUAIHAIZ PU white shoes xRwAa7qZn1, 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 frustumConnect Women's Running Blue Wave Mizuno Shoes .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Running Shoes Women's Connect Wave Mizuno Blue , 2) +Connect Mizuno Women's Wave Shoes Blue Running vp(3, 2); frustum.right.D = -vp(PU Glitter Leather strap Tango X Toe Strap Heel 6cm QJ6133 High Salsa MINITOO Heel Red Latin Ballroom Closed Womens Shoes T Dance qw04wfYg80, 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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