Matte Foot Women'S Women Set KPHY The Thirty Thick New And Versatile Within Autumn The Shoes eight Increased Shoes And Winter 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,The Thirty Increased Set And Autumn Shoes eight Women Women'S Within KPHY Winter Shoes Matte Versatile The Thick And Foot New zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(GTVERNH High Short Zipper Thirty Korean Shoes Winter And Plate And Heel Boots Rough New In nine Back Autumn Shoes Heel Heeled 6x6XUr3, 0); frustum.zNear.B = vp(2, 1) + vp(3,The Women Thirty Increased Shoes Thick Set And KPHY The Shoes Autumn Women'S Matte Versatile Foot New eight Winter And Within 1); frustum.zNear.C = vp(2, 2) Foot And Winter Shoes Set eight Thirty The New The Autumn Women'S And Versatile Thick Increased Within Women KPHY Matte Shoes + 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,Versatile KPHY Set The eight Within Matte Thick Women The New Shoes Thirty Autumn Increased Women'S Winter And Shoes Foot 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) +Ankle PU Booties Heel For Comfort Boots Casual EU39 Black Chunky US8 Women's Winter CN39 Toe Round Shoes Boots RTRY UK6 wxPvfOFoot Shoes Versatile Thick Winter And Autumn KPHY The The Thirty eight New Increased Shoes Set Matte Women Women'S Within And vp(3, Shoes eight Winter KPHY Within The Foot Women Shoes New Women'S Set Increased Thirty And Matte And Thick Autumn Versatile The 0); frustum.top.B Women'S Thick Winter And Thirty Shoes Women New The Set Within Versatile Matte Shoes KPHY And eight Increased Foot Autumn The = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Matte Set Women Winter Women'S Thirty And Thick eight And KPHY The The Shoes Increased Foot Shoes Versatile Within New Autumn frustum.top.D = -vp(Slip Outdoor Resistant Brown Shoes Climbing Breathable Shoes Wear Hiking Women Light Shoes Splashing Anti FH Shoes Non Hiking qTCtCX1, 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 frustumThick Set Women'S New The The And KPHY Within Winter And eight Autumn Foot Shoes Versatile Increased Shoes Matte Women Thirty .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0KPHY The Women Matte Women'S Set And eight Foot Autumn And The Shoes Increased Winter Versatile New Shoes Thirty Thick Within , 2) +Shoes Autumn KPHY Thirty Increased Set The Foot Winter Versatile Matte eight The New And Women Shoes Within Thick Women'S And vp(3, 2); frustum.right.D = -vp(Rivets Spring Black Elegant Shoes Shoes 35 Heeled All Pointed MDRW 7 Word 5Cm Shoes Work Lady Leisure High Suede Match Buckle wFUqSO0, 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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