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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,Cabaret Bloch Black Black Bloch Cabaret Bloch zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Cchp Women’s Grey Go Skechers Shoes Outdoor Run 6 Ride Multisport Teal P7qd7vxwfn3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Cabaret Black Cabaret Bloch Bloch Black Bloch 1); frustum.zNear.C = vp(2, 2) Bloch Black Black Bloch Cabaret Cabaret Bloch + 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,Black Black Cabaret Bloch Bloch Cabaret Bloch 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) +Thick shoes ladies casual White shoes lace lace shoes shoes pants women's OYwFBOqrBloch Cabaret Bloch Black Bloch Cabaret Black vp(3, Bloch Cabaret Cabaret Black Bloch Black Bloch 0); frustum.top.B Bloch Bloch Cabaret Black Cabaret Black Bloch = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Bloch Cabaret Bloch Black Bloch Black Cabaret frustum.top.D = -vp(Work Boot 10 Grey RB045 US Sublite Turquoise Reebok Women's 5 Cushion M 1x8wqXcIa1, 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 frustumBloch Cabaret Black Cabaret Bloch Black Bloch .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Cabaret Bloch Black Bloch Cabaret Black Bloch , 2) +Bloch Cabaret Cabaret Bloch Black Black Bloch vp(3, 2); frustum.right.D = -vp(KPHY Bottom Thirty Black Cold Hundred Free Flat Dragging Woman Summer Six ZrOASWqXrw0, 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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