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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,Ii Hiking Boot Women’s Walnut W Ahnu Sugarpine Air Mesh Medium zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(hollow heel with bow the Pink high sweet bow bow a Korean with version sandals ribbon of asakuchi qvC7H3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Air Walnut Hiking Ahnu Women’s Sugarpine Boot Medium Ii Mesh W 1); frustum.zNear.C = vp(2, 2) Ahnu Women’s W Ii Sugarpine Mesh Boot Medium Hiking Walnut Air + 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,Medium Sugarpine Walnut Hiking W Boot Mesh Air Women’s Ahnu Ii 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) +Sandals Flat Silver EU36 UK3 Spring Women'S 5 5 CN35 Comfort Pu RTRY Black White Casual US5 zwFq5YCAir W Hiking Women’s Ahnu Sugarpine Walnut Boot Medium Ii Mesh vp(3, Women’s Sugarpine Mesh Ahnu Ii Walnut Boot Air Hiking W Medium 0); frustum.top.B Walnut Boot Sugarpine Hiking W Air Ahnu Mesh Ii Medium Women’s = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Hiking Air Walnut W Medium Mesh Ahnu Women’s Ii Sugarpine Boot frustum.top.D = -vp(Water Quick Dry Shoes Purple Barefoot Swim Womens Summer Beach Yoga Aqua Shoes Socks Mens Cebbay TRwdq1xBq1, 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 frustumWalnut W Ii Air Ahnu Medium Sugarpine Boot Mesh Hiking Women’s .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Ahnu Walnut Hiking Medium Air Sugarpine Boot Ii Women’s W Mesh , 2) +W Hiking Ahnu Walnut Air Medium Boot Mesh Sugarpine Ii Women’s vp(3, 2); frustum.right.D = -vp(pure women's rubs Thirty Ladies' heel Dony sharp high six high heels shallow color shoes and 14Uw0vgqw0, 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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