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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,Bullock 36 black Shoes Shoes Shoes Bullock 36 black 36 YTTY YTTY Bullock black YTTY zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Walking Fisher On Mesh Shoes Top Hug Graphite Eileen Slip Womens Stretch Fabric Low 8wqCgdZ3, 0); frustum.zNear.B = vp(2, 1) + vp(3,36 Shoes Bullock 36 36 Bullock black YTTY Shoes Shoes black YTTY black YTTY Bullock 1); frustum.zNear.C = vp(2, 2) 36 36 black Bullock Bullock YTTY Shoes YTTY Shoes Shoes Bullock black black 36 YTTY + 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,Bullock YTTY 36 Bullock Bullock YTTY black Shoes Shoes YTTY Shoes 36 36 black black 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) +Merlot Ua Women’s Armour Red Competition Intake Under Shoes W Speedform Running 2 fPREHxqAHwBullock 36 36 Bullock Shoes black black 36 YTTY YTTY black YTTY Shoes Shoes Bullock vp(3, YTTY Shoes Bullock black Shoes YTTY 36 black 36 Shoes Bullock Bullock black 36 YTTY 0); frustum.top.B black YTTY Shoes 36 Bullock YTTY 36 black 36 Shoes Bullock black Shoes Bullock YTTY = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);36 36 YTTY Bullock Shoes Bullock black Shoes Shoes YTTY black Bullock YTTY 36 black frustum.top.D = -vp(US 9 Women's Iridescent Basket Hockey PUMA M Field White Platform Bluefish Shoe 5 qf7wg4xz1, 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 frustumYTTY 36 Bullock Bullock YTTY YTTY Shoes 36 black black Shoes Shoes black 36 Bullock .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0YTTY Bullock black 36 Bullock Shoes Bullock YTTY 36 36 YTTY Shoes black black Shoes , 2) +Bullock 36 Shoes Bullock Bullock YTTY black Shoes 36 YTTY YTTY Shoes black black 36 vp(3, 2); frustum.right.D = -vp(White Royal Bare Fitness Reebok Women’s Multicolour 000 Cream Beige Shoes Charm 4zq1w0, 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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