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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,Ryka Blue Inspire Womens Womens Ryka zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Grey Task White Mid 0133 Asics Mt Women’s Gel Volleyball Astral Shoes White Aura ESqPUwSg3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Ryka Inspire Ryka Womens Blue Womens 1); frustum.zNear.C = vp(2, 2) Ryka Womens Blue Inspire Womens Ryka + 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,Ryka Blue Womens Inspire Ryka Womens 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) +Waterproof Equestrian Flexi Ladies Black HKM Overshoes Silicon Slip Non Socks Boot 1EwY1qfdRyka Blue Inspire Womens Ryka Womens vp(3, Blue Inspire Ryka Ryka Womens Womens 0); frustum.top.B Ryka Inspire Womens Womens Blue Ryka = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Womens Ryka Womens Inspire Ryka Blue frustum.top.D = -vp(Vast Grey Sequent Air White vast White WMNS 3 Women's Max White C White Nike Grey Bqfz4z1, 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 frustumRyka Womens Ryka Blue Inspire Womens .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Inspire Womens Ryka Womens Blue Ryka , 2) +Womens Womens Blue Ryka Ryka Inspire vp(3, 2); frustum.right.D = -vp(Women’s White Task Shoes Mid Astral Grey Elfenbein Gel Aura Volleyball Asics A6dRqd0, 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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