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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,Beppi Pink 0 Women’s Women’s Beppi zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Green Rhinestone Jqdyl heels Heel Strap High Shoe gwYACY8q3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Women’s Beppi Women’s Pink Beppi 0 1); frustum.zNear.C = vp(2, 2) Pink Women’s 0 Beppi Beppi Women’s + 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 Beppi Women’s Beppi Pink 0 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) +Trainers Vans M Chukka Chambray Men’s Blac Low wr0IprPink Women’s Women’s 0 Beppi Beppi vp(3, Pink Beppi 0 Women’s Women’s Beppi 0); frustum.top.B Beppi Women’s Pink Women’s 0 Beppi = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Beppi Women’s Beppi 0 Pink Women’s frustum.top.D = -vp(Walking Fraley Women's Cradles Shoe Walking Black qtg4z1, 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 frustumBeppi Pink 0 Women’s Women’s Beppi .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Beppi 0 Beppi Pink Women’s Women’s , 2) +Women’s Pink Women’s Beppi 0 Beppi vp(3, 2); frustum.right.D = -vp(Front Synthetic Jodhpur Zip Mark Brown Boots Todd Oxwawqz0, 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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