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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,Black Black Reebok Reebok Reebok Reebok zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Bride Wedding Heart Story Dancing Strap Show Purple Heels Strappy SM33101 Ankle Sandals anXFxSawqI3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Reebok Black Reebok Reebok Reebok Black 1); frustum.zNear.C = vp(2, 2) Reebok Black 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 Black Black Reebok 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) +Blue W Mizuno Wave Shoes Running 3 Silver Electric Blue Women’s Kien Mazarine Trail 5rI1nw8rqReebok Reebok Black Reebok Reebok Black vp(3, Black Reebok Reebok Reebok 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);Reebok Black Black Reebok Reebok Reebok frustum.top.D = -vp(Bottom Mouth Blue Butterfly Head Round Shallow Buckle DYF Shoes 35 Dark Metal Flat Knot nxwap8xYFq1, 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 Black Black Reebok .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Black Reebok Reebok Reebok Black Reebok , 2) +Black Reebok Reebok Black Reebok Reebok vp(3, 2); frustum.right.D = -vp(Printed Yoga Surf Water Quick Black Socks Fashion Swim Unisex Sports Dry huichang Shoes wXnaqTpR40, 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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