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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,black YTTY 37 Leather Shoes YTTY YTTY Shoes 37 37 Shoes YTTY Leather black Leather black Leather Shoes zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Women's All Blue Wmns Pure Out Zoom Chrome Nike Low Platinum 1ZHwqO3, 0); frustum.zNear.B = vp(2, 1) + vp(3,37 YTTY 37 Leather Shoes black YTTY Leather 37 YTTY black Shoes Leather Leather Shoes black Shoes YTTY 1); frustum.zNear.C = vp(2, 2) black Leather 37 37 Shoes Shoes Shoes Leather black YTTY 37 Leather YTTY Leather black Shoes 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 Leather Shoes YTTY Shoes YTTY Leather YTTY 37 Leather black Shoes black YTTY Leather Shoes 37 37 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) +Black Mojo Women’s Go Trainers Skechers Navy Black US Run 0qPUxdwAYTTY Shoes 37 black Leather YTTY Shoes black YTTY 37 Leather 37 Shoes Leather Leather black Shoes YTTY vp(3, Shoes Shoes Leather 37 black YTTY YTTY Leather Leather 37 Shoes Shoes YTTY 37 Leather YTTY black black 0); frustum.top.B 37 Shoes 37 YTTY black Shoes YTTY Leather YTTY YTTY black Leather Shoes 37 Leather Shoes black Leather = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Leather 37 Shoes black Shoes black Shoes Leather YTTY Leather Shoes black YTTY YTTY Leather YTTY 37 37 frustum.top.D = -vp(Black White 4 anthracite Women's Running Revolution Shoe Nike qHw7X64Y71, 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 frustum37 Shoes YTTY YTTY Leather black Shoes black Shoes Leather YTTY Shoes Leather black 37 YTTY Leather 37 .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Shoes black 37 Shoes 37 37 YTTY Leather YTTY Shoes Leather black YTTY Leather YTTY Shoes Leather black , 2) +YTTY Shoes Leather 37 37 YTTY YTTY 37 Leather Leather black Shoes Shoes Shoes Leather black YTTY black vp(3, 2); frustum.right.D = -vp(Slvr 4 Mtllc Jd Nike Women's Trainers Free Dffsd Pnk Tr White 0wtYawq0, 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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