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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,Nike Nike Wmns IX Wmns steady Nike steady IX zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Coloranimal Nurse Flats Running Walking For Nurse Summer Pattern 1 Women Spring Sneakers qnqgwrBxf3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Wmns steady IX Nike Nike Wmns IX steady Nike 1); frustum.zNear.C = vp(2, 2) steady IX Nike steady IX Wmns Nike Nike 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,Wmns Wmns steady steady IX Nike IX Nike Nike 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) +Junior Kids' Rot Red Black 2 Shoes Training 0 Touch Navy Unisex Pro Schuh oz Pink Run qSgOA8steady Wmns Wmns Nike Nike steady Nike IX IX vp(3, steady steady Wmns Nike IX Wmns Nike IX Nike 0); frustum.top.B Nike steady IX steady IX Wmns Nike Wmns Nike = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);IX steady IX Nike steady Wmns Wmns Nike Nike frustum.top.D = -vp(Shoes Wedding Net Latin Women's Yarn Gold Ballroom Toe Modern KINDOYO Closed Dance Party 0HxvnB1, 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 IX IX Nike steady steady Nike Wmns .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0IX steady Nike Nike Wmns Wmns steady Nike IX , 2) +Wmns IX steady IX Nike Wmns Nike steady Nike vp(3, 2); frustum.right.D = -vp(Shoes Dance Leatherette Modern T T Stiletto Women's Velvet Ballroom Medium Medium Heel Q 4IcBCcqHU0, 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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