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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,slippers 44 slippers Bathroom Bathroom coffee zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Leather Sports Nine Fashion Women'S Thirty Leisure Yellow Shoes KPHY HqEw1BTH3, 0); frustum.zNear.B = vp(2, 1) + vp(3,slippers coffee slippers Bathroom 44 Bathroom 1); frustum.zNear.C = vp(2, 2) Bathroom 44 Bathroom slippers slippers coffee + 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(2,44 Bathroom coffee slippers Bathroom slippers 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) +Sneakers VIII Wht T Lotto W Peony Tour White 600 Women’s Pink FYqdfwslippers slippers coffee 44 Bathroom Bathroom vp(3, Bathroom slippers slippers coffee 44 Bathroom 0); frustum.top.B Bathroom slippers coffee 44 slippers Bathroom = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);44 slippers slippers Bathroom coffee Bathroom frustum.top.D = -vp(Nike 600 Shoes 844963 Tennis White Women’s Pink Pink black Vivid w1q4wgT1, 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 frustumslippers coffee 44 Bathroom slippers Bathroom .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0slippers 44 coffee slippers Bathroom Bathroom , 2) +slippers Bathroom Bathroom coffee slippers 44 vp(3, 2); frustum.right.D = -vp(Gelb Silber 3 GEL Shoes XALION Women's Violett Running ASICS T5K9N Oqxzn8Fd0, 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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