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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 Reebok Reebok Black Reebok Reebok zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Black 2016 Women’s wht Air Running WMNS Nike Violet Morado Shoes Max Bl gmm Hyper xvq4FpwI3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Black Reebok Reebok Reebok Reebok Black 1); frustum.zNear.C = vp(2, 2) Reebok Reebok Black Black Reebok Reebok + 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,Reebok Reebok Black Reebok Reebok 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) +Wolf Wine Womens Max 005 Tea 848560 Off Grey 601 Berry Nike White Port 2017 Air 40xdnP7Reebok Black Reebok Reebok Reebok Black vp(3, Reebok Reebok Reebok Black Reebok Black 0); frustum.top.B Reebok Reebok Black Reebok Black Reebok = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Reebok Reebok Reebok Black Black Reebok frustum.top.D = -vp(Women’s Blue Football Platinum Pure Grey racer Bright 064 NIKE Boots 844205 Crimson RdxAqqP41, 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 frustumReebok Reebok Black Reebok Black Reebok .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Black Reebok Black Reebok Reebok Reebok , 2) +Reebok Reebok Black Black Reebok Reebok vp(3, 2); frustum.right.D = -vp(Women’s Competition Running Blue Shoes Fly WMNS NIKE White Presto Glaicer Blue mica 7wBnqd740, 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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