Terrain Black Black Ariat Chap Ariat Terrain II II Chap 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,Black II Terrain Chap Terrain Chap Black II Ariat Ariat zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Women’s 553137c Converse 12 Trainers Black UK Blue v1xTSw73, 0); frustum.zNear.B = vp(2, 1) + vp(3,II Chap Chap Black Black II Terrain Ariat Terrain Ariat 1); frustum.zNear.C = vp(2, 2) Black Black Ariat Ariat Terrain Chap Terrain Chap II II + 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,Terrain Chap Ariat II Ariat Chap Terrain Black II Black 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 Kampala W MBT Brown Women’s Coffee Brown xtw5qR5fTerrain Black Terrain II Chap Black Ariat Chap II Ariat vp(3, Black II Terrain Ariat Ariat Chap Chap Terrain Black II 0); frustum.top.B Chap Ariat Chap Ariat Terrain Black II Black II Terrain = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Chap Terrain Ariat II Chap Terrain Ariat Black II Black frustum.top.D = -vp(White Superstar 3 5 UK adidas Boys' White Trainers CqxgwCOf71, 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 frustumChap Chap Ariat Terrain Black Ariat Black II Terrain II .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Ariat Black Terrain II Terrain Chap Chap II Black Ariat , 2) +Black Terrain Chap II Chap Black Ariat Ariat Terrain II vp(3, 2); frustum.right.D = -vp(Women’s Trainers Grey Gioseppo Grey 43 Grey Alana 7zEzdnBqw0, 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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