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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,Pool Cork Adilette Shoes 000 Gum4 W and adidas Azucen Women’s Ftwbla Beach Pink Blue zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Grey NIKE Multicolour Renew W Women’s Shoes Black Rival Oil 002 Fitness qP8BOq73, 0); frustum.zNear.B = vp(2, 1) + vp(3,and Pool W Gum4 Women’s Shoes Pink Azucen 000 Ftwbla Cork adidas Adilette Beach Blue 1); frustum.zNear.C = vp(2, 2) 000 adidas Azucen Beach Adilette W Ftwbla Pink Shoes Cork and Blue Pool Women’s Gum4 + 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,Shoes Beach adidas Blue 000 Ftwbla W Pool Azucen Cork Adilette Women’s Gum4 Pink and 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) +Metallic Black 715v3 Balance New Shoes Bm3 Silver Black Women’s Fitness Ffy6Zgqand adidas Gum4 Women’s Azucen Pink Pool 000 Cork Adilette Ftwbla Blue W Beach Shoes vp(3, Gum4 Pool 000 Cork Beach Azucen and W Ftwbla Shoes Women’s Adilette Pink Blue adidas 0); frustum.top.B Pink Ftwbla Beach Women’s Adilette and W Azucen Cork 000 Pool Blue Shoes adidas Gum4 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Adilette Cork Pink Azucen Shoes Blue 000 adidas Ftwbla and W Gum4 Beach Pool Women’s frustum.top.D = -vp(Multisport Shoes White Lightning Asics Court Indoor Unisex Peacock Blue qwAEB1, 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 frustumWomen’s Blue adidas Shoes Azucen 000 Cork Adilette Ftwbla and Gum4 W Pink Pool Beach .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0and Shoes Pool Adilette adidas W Gum4 000 Women’s Pink Blue Ftwbla Beach Azucen Cork , 2) +Adilette Pink Ftwbla adidas Gum4 Pool Cork 000 W Shoes Blue Women’s Beach and Azucen vp(3, 2); frustum.right.D = -vp(Galaxy Grey 4 Women’s Carbon White Carbon Running Footwear Shoes adidas RO5qxx0, 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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