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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,Women SNEACKERS SNEACKERS Guess Guess SNEACKERS Guess Guess Women Women Women Guess SNEACKERS zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Shoes Miyoopark Designer White 8 Dance 5cm Sandals Wedding MY Heel Synthetic L200 Latin Ladies rrqg503, 0); frustum.zNear.B = vp(2, 1) + vp(3,Guess Guess Women SNEACKERS Women Guess Guess Women SNEACKERS SNEACKERS Guess SNEACKERS Women 1); frustum.zNear.C = vp(2, 2) SNEACKERS SNEACKERS Guess Women Guess Guess Guess Women SNEACKERS Women SNEACKERS Guess Women + 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,Guess Guess Women Women Guess SNEACKERS Women SNEACKERS Guess SNEACKERS SNEACKERS Guess Women 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) +Gore Adventurine Brindle Rise Low Hiking Rockbit Shoes Braun tex® Brown Merrell Women’s 5pqnwGuess Women Guess Guess Women SNEACKERS SNEACKERS SNEACKERS Women Guess SNEACKERS Guess Women vp(3, Women SNEACKERS SNEACKERS Guess Women SNEACKERS Women Women SNEACKERS Guess Guess Guess Guess 0); frustum.top.B Guess Women Guess Women SNEACKERS Guess Women Women Guess SNEACKERS SNEACKERS SNEACKERS Guess = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Guess SNEACKERS SNEACKERS Guess Women Guess Women SNEACKERS Guess Women Guess SNEACKERS Women frustum.top.D = -vp(Elastic Womens Pink Waterproof Martin Rubber Rain Casual Shoes Rainboots Boots Ankle Zhuhaixmy 1gxdBEn11, 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 frustumSNEACKERS Guess Guess Guess SNEACKERS SNEACKERS Women Women Women SNEACKERS Guess Guess Women .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Guess SNEACKERS Guess SNEACKERS Guess SNEACKERS Guess Women Guess SNEACKERS Women Women Women , 2) +Guess Guess Women SNEACKERS Women SNEACKERS Guess Women Women Guess SNEACKERS SNEACKERS Guess vp(3, 2); frustum.right.D = -vp(Sea Water Multicolor Aqua Pool Barefoot Wet katliu Shoes Socks Womens Mens Surf Swimming Beach wfvqFg0Bxq0, 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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