Walking Comfort 1TO9 Shoes Womens MMS06280 Assorted Colors Green Urethane Platform 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,MMS06280 Womens Walking Green Colors Urethane 1TO9 Assorted Platform Comfort Shoes zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(boots heel side Ladies heel big in zipper Pink round short size winter XRwwqUxv3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Urethane Comfort Platform Assorted Womens Shoes MMS06280 Green Colors Walking 1TO9 1); frustum.zNear.C = vp(2, 2) MMS06280 Platform Shoes 1TO9 Green Walking Colors Comfort Assorted Womens Urethane + 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,MMS06280 Urethane 1TO9 Shoes Walking Womens Colors Comfort Assorted Green Platform 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) +Hiking Shoes 6 Size M Helvatia Womens YL5096051 5 Columbia Shale Synthetic Sw1f5qHShoes Green 1TO9 MMS06280 Assorted Colors Womens Urethane Platform Walking Comfort vp(3, MMS06280 Womens Comfort Urethane Colors Assorted Shoes Green 1TO9 Platform Walking 0); frustum.top.B Womens Green MMS06280 Urethane Comfort Colors 1TO9 Assorted Shoes Walking Platform = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Platform Colors Assorted Green Shoes Urethane Womens MMS06280 1TO9 Walking Comfort frustum.top.D = -vp(CHAQLIN Trail 8 cat Shoes Cute Breathable Cat Black Sneakers Pattern Women HPHTBqSwr1, 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 frustumAssorted Comfort Shoes 1TO9 Platform Urethane Womens Green Walking MMS06280 Colors .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0MMS06280 Platform Colors Comfort 1TO9 Womens Urethane Green Walking Assorted Shoes , 2) +Womens Shoes Assorted Green 1TO9 MMS06280 Comfort Colors Walking Platform Urethane vp(3, 2); frustum.right.D = -vp(Fitness Under Micro 001 Shoes Black Press Women’s Black Tr Ua G Armour W rIpHw8xrq0, 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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