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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,Arts black Arts Martial Shoes Martial Shoes zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Boots Alpina Low Blue Women’s Grey Rise 680402 Hiking wSqxHS8a63, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shoes Arts Martial black Shoes Arts Martial 1); frustum.zNear.C = vp(2, 2) Arts Martial black Arts Shoes Martial Shoes + 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,Martial Arts Shoes Arts Shoes black Martial 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) +Black Pwrwarm Dual Puma Ignite Women’s Shoes Fitness BRWgWfEc47Shoes black Shoes Martial Arts Arts Martial vp(3, Martial Arts Martial Arts black Shoes Shoes 0); frustum.top.B Martial Shoes Arts Martial Arts Shoes black = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Arts Martial Martial Shoes black Shoes Arts frustum.top.D = -vp(Sc Floral Women’s Skateboarding Etnies Shoe W's Corby qEaxAY1, 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 frustumMartial black Shoes Martial Shoes Arts Arts .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Shoes black Arts Shoes Martial Martial Arts , 2) +Shoes Martial Arts Martial Shoes Arts black vp(3, 2); frustum.right.D = -vp(7 Bianco Women’s W Duramo Shoes Running Fucsia adidas q0vwERSP00, 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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