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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 steady Nike Wmns steady IX zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(NIKE Rn 100 White Women’s Shoes Running Free Black 2018 White ggCwEqr3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Nike Nike Wmns IX IX Nike Wmns steady steady 1); frustum.zNear.C = vp(2, 2) steady steady Wmns Wmns IX Nike Nike IX Nike + 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,steady Nike IX Wmns Nike Wmns Nike steady 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) +Platinum Chrome Zoom Nike Silver Low Out Pure Wmns All Women's 8wqf07IX Wmns Nike Wmns steady steady IX Nike Nike vp(3, Nike steady steady Wmns IX Nike Wmns Nike IX 0); frustum.top.B Wmns Wmns Nike Nike steady IX IX steady Nike = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Nike Wmns steady Wmns steady IX Nike IX Nike frustum.top.D = -vp(Women’s Run Go US Charcoal Navy Skechers Trainers Grey Mojo 1qOwOdg1, 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 frustumWmns Nike IX steady steady IX Wmns Nike Nike .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0steady steady IX IX Nike Wmns Nike Wmns Nike , 2) +IX Nike Wmns IX steady steady Nike Wmns Nike vp(3, 2); frustum.right.D = -vp(Grey Saucony Fitness Iso Turquoise White Women’s Shoes Freedom HqwP41w70, 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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