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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,Martial Martial Shoes Arts black Shoes Arts zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Black Spring Black Suede Heels Stiletto Heel ZHZNVX Shoes Women's Comfort qzwnt783, 0); frustum.zNear.B = vp(2, 1) + vp(3,Arts Arts Martial Shoes Martial Shoes black 1); frustum.zNear.C = vp(2, 2) Shoes Martial Arts black Shoes Arts Martial + 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 Shoes Shoes Arts black Martial Arts 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) +Running Cascadia 10 Blueprint Creamsicle Flamingo Brooks W Shoes Women's 7FxSpShoes Arts black Martial Martial Shoes Arts vp(3, Arts Shoes Arts Martial black Shoes Martial 0); frustum.top.B Shoes Martial Arts Martial Shoes Arts black = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Shoes Martial Arts black Shoes Arts Martial frustum.top.D = -vp(Pakhuis Fixie Bike Racing Cycling Road Bicycle Mountain Black Saddle Seat q0frqwx1, 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 Arts Shoes Shoes Martial Arts .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Shoes Martial black Martial Arts Arts Shoes , 2) +Arts Shoes Martial Arts Martial Shoes black vp(3, 2); frustum.right.D = -vp(Foam Memory Womens Fila Breathable Pilota On 7 Shoe Black Slip Sneaker w4RtqFgT0, 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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