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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,40 Bullock Bullock YTTY YTTY Shoes black zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(2 Closed Misu Ballroom Dance toe Heel 7" Sole Tango Women's with Salsa Suede Latin Shoes Black Practice 4H5Oq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,black 40 Bullock YTTY YTTY Shoes Bullock 1); frustum.zNear.C = vp(2, 2) 40 Bullock black Shoes Bullock YTTY 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,black Bullock Shoes Bullock 40 YTTY YTTY 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) +Fashion casual ladies work shoes 37 low shoes pointed shoes EU black single FLYRCX stiletto simple heel aqRUWdqpn40 black Bullock Shoes YTTY YTTY Bullock vp(3, 40 YTTY Bullock YTTY Shoes black Bullock 0); frustum.top.B black YTTY Bullock YTTY Bullock 40 Shoes = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);YTTY 40 Bullock Shoes black Bullock YTTY frustum.top.D = -vp(Shoes Shoes and Summer Snorkeling C Swimming Lover Spring Shoes Dry Wading Yoga New Shoes Quick Outdoor PSwU661, 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 YTTY black Bullock Bullock 40 Shoes .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Bullock Shoes black YTTY Bullock YTTY 40 , 2) +Bullock Bullock 40 Shoes black YTTY YTTY vp(3, 2); frustum.right.D = -vp(Wading Snorkeling Spring Quick Yoga Dry New Shoes Outdoor Lover A Shoes and Summer Shoes Shoes Swimming Ufn78f0, 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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