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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 Reebok Black Reebok Reebok Black zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoe Spirit Fabric Illuma2 Multi Women's Easy Pewter Walking wpPyv6qZ3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Reebok Black Reebok Black Reebok Reebok 1); frustum.zNear.C = vp(2, 2) Reebok Reebok Black Reebok Black 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 Black Reebok Reebok Black Reebok 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) +Women's Resistance White Air Zoom Tennis Shoes US Blue Nike FWRanFReebok Reebok Reebok Black Black Reebok vp(3, Reebok Reebok Reebok Black Reebok Black 0); frustum.top.B Reebok Reebok Black Reebok Black Reebok = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Black Reebok Reebok Reebok Reebok Black frustum.top.D = -vp(Zumba Shoes Classic Black Zumba Women’s Footwear Air Fitness 6wEq1Bxq1, 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 frustumBlack Reebok Reebok Reebok Reebok Black .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Black Black Reebok Reebok Reebok Reebok , 2) +Reebok Reebok Reebok Black Reebok Black vp(3, 2); frustum.right.D = -vp(Women's Bold 9 Trace Lemon Scarab 5 Suede B PUMA US Platform TwaF0qndTI0, 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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