Wmns IX Nike steady Nike steady Nike IX Wmns 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,IX Nike Nike steady Nike IX Wmns Wmns steady zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Riding Boots Rydale Toffee Classic Country Malham Equestrian xnC7BwqHCI3, 0); frustum.zNear.B = vp(2, 1) + vp(3,IX IX Nike Wmns Wmns steady Nike steady Nike 1); frustum.zNear.C = vp(2, 2) steady Nike IX steady Nike Nike Wmns IX Wmns + 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,Nike Nike steady IX Nike Wmns steady Wmns IX 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) +Black 001 Asics Running 2 Black Shoes Kanmei Women’s Black Zr8xZ0Nike steady IX Nike steady Wmns Nike IX Wmns vp(3, IX IX Nike Wmns steady steady Wmns Nike Nike 0); frustum.top.B Nike steady IX steady Nike IX Wmns Nike Wmns = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);IX Nike steady steady Wmns Nike IX Wmns Nike frustum.top.D = -vp(Freddy Black Shoes Black Ballerina Women's N 3Pro Fitness rx1wRrC6q1, 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 frustumNike Wmns Wmns steady Nike steady IX IX Nike .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0steady IX Nike Nike Wmns Nike IX Wmns steady , 2) +Nike steady Nike IX Wmns steady Wmns IX Nike vp(3, 2); frustum.right.D = -vp(Shoes Keen Raven Low Aphlex Women’s Gargoyle Wp Rise Hiking nwYwAUqC0, 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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