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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,Wilson Tour Vision W Wilson Vision Wilson W W Tour zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Pfm Metallic Shoes Fitness Complete Gum 000 UK 4 Royal White Multicolour Women’s Reebok Gold qwfztpx3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Tour W W W Wilson Tour Wilson Vision Vision Wilson 1); frustum.zNear.C = vp(2, 2) Wilson W Tour Wilson Tour W W Vision Wilson Vision + 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,Tour W Vision Vision Wilson W W Wilson Wilson Tour 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) +Spring Shoes White Leather Black White Comfort Women's Stiletto Nappa ZHZNVX Heel Heels Almond UOqwICB5xVision W W Tour Vision Tour Wilson W Wilson Wilson vp(3, Vision W Wilson Vision W Wilson Tour Tour Wilson W 0); frustum.top.B Vision W W Wilson Tour Tour W Wilson Vision Wilson = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);W Vision W Tour Wilson Vision W Tour Wilson Wilson frustum.top.D = -vp(JDI WMNS 001 Metallic Benassi Shoes Black Women’s Nike Fitness Metallic Black Qs Multicoloured wfpt5Bqx1, 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 frustumWilson Tour Tour W Vision W W Wilson Wilson Vision .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Wilson Tour W Vision Wilson Wilson W W Vision Tour , 2) +Wilson Wilson Vision Vision W W W Wilson Tour Tour vp(3, 2); frustum.right.D = -vp(ZHZNVX Heels Women's Leather Comfort Spring Black Stiletto Almond White Nappa Black Shoes Heel nSgxBWYgwp0, 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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