V Velocity Women's Women's Women's Velocity V Velocity V 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,V Velocity Velocity V Velocity V Women's Women's Women's zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(White pink V6 navy 11fg Boots Adult Puma YRHqfwIq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,V Women's V Velocity V Women's Women's Velocity Velocity 1); frustum.zNear.C = vp(2, 2) Velocity V Women's Velocity V V Velocity Women's Women's + 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,V Women's Velocity V Velocity V Velocity Women's Women's 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) +Zalock 2 Black Women's Size Shoes Water UwpArqUfVelocity Women's Women's V Women's Velocity V V Velocity vp(3, Velocity Velocity Women's Velocity V Women's Women's V V 0); frustum.top.B Velocity Women's Velocity V Women's Women's V V Velocity = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);V Velocity Velocity V Women's V Women's Women's Velocity frustum.top.D = -vp(Dark Lady brown GTX Eiffel yellow Meindl 50pxTwE1, 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 frustumVelocity Velocity V V Women's Velocity V Women's Women's .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0V V Women's Velocity Velocity Velocity Women's V Women's , 2) +Women's Women's Velocity Velocity Velocity V Women's V V vp(3, 2); frustum.right.D = -vp(Autumn Women'S Beige Winter And In Boots xEqEO4R0, 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.