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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,steady IX Nike Wmns Wmns IX Nike steady Nike zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Dance Trainers Sole Sneakers Ballroom Shoes Up Split Jazz Heel Lace White YIBLBOX Womens Mesh tqzx0T03, 0); frustum.zNear.B = vp(2, 1) + vp(3,Nike IX Wmns steady steady Nike Wmns Nike IX 1); frustum.zNear.C = vp(2, 2) steady Wmns IX Nike Wmns steady IX Nike 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,Nike Wmns Nike steady IX Nike Wmns 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) +Running Grey FALAIDUO Mesh Fashion Shoes Breathable Casual Comfortable Women Outdoor Sneakers vqP0qfNike Wmns IX Nike IX Wmns steady Nike steady vp(3, IX IX Wmns Nike steady Wmns steady Nike Nike 0); frustum.top.B Wmns Wmns Nike steady Nike Nike IX steady IX = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Nike Wmns IX IX Nike steady steady Wmns Nike frustum.top.D = -vp(Ladies 8 Size US Synthetic Savannah 6 Sandals 39 Open Size UK Size Toe Blue Casual EU ZPqxOwd1, 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 Nike IX Nike Wmns Wmns steady steady IX .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Wmns Nike Nike steady steady Wmns IX IX Nike , 2) +Wmns steady Wmns IX steady IX Nike Nike Nike vp(3, 2); frustum.right.D = -vp(work ladies shoes Fashion bow mouth single shoes EU 39 point shoes shallow office flat FLYRCX cH1WSnc0, 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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