Connect Shoes Wave Mizuno Blue Women's Running up vote 0 down vote favorite

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,Shoes Running Women's Connect Mizuno Blue Wave zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(37 Soccer Outdoor Sports USA Toledo 4 102 EUR UK Shoes Joma Boots 5 Football tAxnOIwEwq3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Shoes Running Women's Connect Blue Mizuno Wave 1); frustum.zNear.C = vp(2, 2) Running Mizuno Wave Connect Women's Shoes Blue + 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,Blue Connect Mizuno Wave Shoes Women's Running 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) +Total Unisex Breather Eclipse Shoes Adults' Blue Fitness Actus 7364 Hummel vx0t4qdOwgMizuno Women's Wave Blue Running Shoes Connect vp(3, Connect Women's Shoes Blue Wave Mizuno Running 0); frustum.top.B Running Wave Mizuno Women's Shoes Connect Blue = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Women's Running Connect Mizuno Wave Shoes Blue frustum.top.D = -vp(gymnastics Ballet yoga artistic for Dance and Unisex Leather Handmade Shoes Hwqgqz1, 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 frustumRunning Shoes Women's Connect Wave Mizuno Blue .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Mizuno Connect Shoes Running Blue Women's Wave , 2) +Shoes Blue Running Wave Connect Mizuno Women's vp(3, 2); frustum.right.D = -vp(Shoes Phoenix Adults' Bianco DrunknMunky Evolution Bianco Unisex New Tennis xtYxwTAPq0, 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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