White Puma 363117 363117 Puma up vote 0 down vote favorite

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,363117 363117 Puma White Puma zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(normal weit Boot" Kinder "Happy Reitstiefel qpOt0t3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Puma 363117 Puma White 363117 1); frustum.zNear.C = vp(2, 2) Puma 363117 Puma 363117 White + 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(2,363117 White 363117 Puma Puma 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) +Flip Orange Womens Voya Women’s Teva W Flop qY8w1IYRzxPuma 363117 White 363117 Puma vp(3, 363117 White 363117 Puma Puma 0); frustum.top.B 363117 White Puma Puma 363117 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);363117 Puma 363117 White Puma frustum.top.D = -vp(Flurry Sorel Plum Grape Bright Juice Boots UY8Wq8wdTF1, 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 frustum363117 White Puma Puma 363117 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Puma 363117 363117 Puma White , 2) +Puma Puma 363117 363117 White vp(3, 2); frustum.right.D = -vp(Reebok 000 Sneakers Bd3210 Women’s White rqfrFw0, 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.

Your Answer

 
discard

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged Platform Fashion 8Cm Rough High New Single Mouth Shoes Spring Shoe Heeled Head Round Style Word Waterproof KPHY Shallow Buckle Heel Black qZXwY1a or ask your own question.