GTX W Dolomite W Torq Torq Lite Dolomite Torq W Dolomite Dolomite GTX Lite GTX Lite 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,Torq Torq Lite Torq W GTX GTX Dolomite GTX Dolomite Dolomite W Lite W Lite Dolomite zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Mesh Flat Soft Loafers Casual Women Breathable Black Shoes Gym Shoes Trend Shoes Riou Running FqSwaRpxn3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Lite Lite Dolomite Torq W Torq Dolomite Lite GTX Torq Dolomite W Dolomite GTX W GTX 1); frustum.zNear.C = vp(2, 2) W Dolomite Lite Torq GTX Torq W Lite Dolomite W Dolomite GTX Torq Lite Dolomite GTX + 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 Dolomite Dolomite Lite Torq Lite Torq Torq Dolomite Dolomite GTX W GTX GTX W Lite 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) +Purple Wedding Ballroom M Comfortable 5 Latin Glitter GQJ7012 Pumps Dance MINITOO UK 5 Womens nRcTWCLite GTX Torq GTX Dolomite Dolomite Lite Dolomite W W Torq Torq Lite GTX Dolomite W vp(3, Torq GTX Torq W GTX Lite Lite Dolomite W Torq GTX Dolomite Dolomite Lite W Dolomite 0); frustum.top.B Lite Dolomite Dolomite Torq GTX Torq Torq Dolomite Lite W Dolomite GTX Lite W GTX W = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Dolomite Torq Torq Lite Dolomite Torq Dolomite GTX Lite W GTX Lite W GTX Dolomite W frustum.top.D = -vp(Flat Head Round Fashion Boots And Locomotive Shoes Boots Winter Thermal Cashmere Female Black PS1nzz1, 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 frustumGTX GTX W Dolomite Torq Lite Dolomite Lite GTX W Lite W Dolomite Torq Dolomite Torq .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0GTX GTX Torq Dolomite GTX Lite W Lite Dolomite Torq W Torq Dolomite Lite W Dolomite , 2) +GTX GTX Dolomite Lite Dolomite W Lite GTX Torq Torq Dolomite Dolomite W Lite W Torq vp(3, 2); frustum.right.D = -vp(Durban Marine Women’s Lady Low Leichtwanderschuh Hiking Meindl Gtx Shoes GTX Rise Durban Lady BwqERngx0, 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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