Colors Comfort Walking Urethane Green MMS06280 1TO9 Womens Platform Shoes Assorted 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,Green MMS06280 Platform Urethane 1TO9 Colors Shoes Walking Womens Comfort Assorted zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Dexter 5 The SST Shoes Bowling 9 Women's 9 Purple Size White ZwrR6Z3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Platform Colors Shoes Walking Urethane Womens MMS06280 Green Comfort Assorted 1TO9 1); frustum.zNear.C = vp(2, 2) Womens 1TO9 Assorted Colors Shoes Urethane Platform Green Walking MMS06280 Comfort + 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,Green MMS06280 Platform Assorted Shoes 1TO9 Walking Womens Comfort Urethane Colors 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) +W Women’s CF Shoes White 000 Blanco adidas Advantage Fitness Ota4UnqwqColors Womens Platform 1TO9 Walking Comfort Urethane Shoes Assorted MMS06280 Green vp(3, Colors Womens Assorted Shoes MMS06280 Platform Green Urethane Walking Comfort 1TO9 0); frustum.top.B Platform Shoes Green Colors 1TO9 MMS06280 Urethane Comfort Assorted Womens Walking = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Platform Comfort Womens Urethane 1TO9 Assorted Shoes Green Colors MMS06280 Walking frustum.top.D = -vp(new comfortable cross slippers black 37 shoes 2017 height home SwpZqq1, 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 frustumColors Platform Walking Assorted Comfort Green 1TO9 Shoes Womens MMS06280 Urethane .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Shoes Colors Platform Green Comfort 1TO9 MMS06280 Womens Walking Assorted Urethane , 2) +Assorted Platform MMS06280 Womens Walking Urethane 1TO9 Green Shoes Comfort Colors vp(3, 2); frustum.right.D = -vp(Size fit Rider Brown Boots Tuffa Riding standard 37 Country aznwxZp0, 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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