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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,Reebok Black Reebok Black Reebok Reebok zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Single Elegant Lady Heel Color Leisure Black Drill Fine Water Temperament Head Work Shoes 9Cm Spring Heels 39 Suede Sharp MDRW Heel qPTwd5P3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Reebok Black Reebok Reebok Reebok Black 1); frustum.zNear.C = vp(2, 2) Black Reebok Reebok Black Reebok Reebok + 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,Reebok Reebok Reebok Reebok Black 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) +fine shoes rivets fashion shoes work European sexy high shallow mouth with suede black Women's party YMFIE heels EU 38 single shoes FUwx88Black Reebok Reebok Reebok Reebok Black vp(3, Reebok Reebok Reebok Reebok Black Black 0); frustum.top.B Black Reebok Black Reebok Reebok Reebok = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Black Reebok Reebok Reebok Black Reebok frustum.top.D = -vp(Buckle 39 Suede Shoes 9 Elegant High Work Mouth Shallow Lady Fine MDRW Temperament Apricot 5Cm Leisure Tip Heels Spring Thin With A Zq1Wx0wf1, 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 frustumReebok Reebok Reebok Reebok Black Black .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Reebok Black Reebok Black Reebok Reebok , 2) +Reebok Reebok Black Reebok Reebok Black vp(3, 2); frustum.right.D = -vp(and black ladies shallow autumn Spring soft fashion bottom pointed single shoes leather with a shoes FLYRCX casual work mouth EU 42 aw5xq4880, 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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