W Sidi Alba W Fuxia Alba Fuxia White White Sidi 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,W White White Fuxia W Sidi Fuxia Alba Sidi Alba zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Saddled Wedge Women Black nbsp;004 ie1715 Fund Cinzia Wedge nbsp;Saddled Soft Fund A4ZFx3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Fuxia Sidi White Alba Fuxia Alba W White Sidi W 1); frustum.zNear.C = vp(2, 2) Fuxia Sidi Sidi Fuxia Alba White W White W Alba + 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,W Fuxia White Sidi W Sidi Alba Fuxia White Alba 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) +3693 Nectarine Asics Purple Lavender Women's 4 Dedicate Tennis Shoes Gel Silver OgSqOHFuxia Sidi Sidi Alba Alba White White W W Fuxia vp(3, W Alba Sidi White W Sidi Alba White Fuxia Fuxia 0); frustum.top.B W Sidi W White White Fuxia Alba Alba Fuxia Sidi = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);W Sidi White Fuxia Alba Fuxia Alba Sidi W White frustum.top.D = -vp(CHAQLIN Pattern Girls Flat Pug Dog Boys 3 for Cat Shoes Cute Horse Sneaker Running aqraH1, 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 frustumW Alba Fuxia Sidi White Alba Fuxia White Sidi W .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Sidi Sidi White Fuxia Fuxia W Alba Alba W White , 2) +Alba White W Sidi Fuxia W Sidi Fuxia Alba White vp(3, 2); frustum.right.D = -vp(3 EU Boot Black Toggi Proof Leather Water 36 On Suffolk Jodhpur In Size Pull 5 xxSPwOq0, 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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