Terrain II Ariat Chap II Ariat Terrain Black Chap Black 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,Ariat Chap Chap II Terrain Ariat Terrain Black Black II zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(5 Stiletto Combat Fashion Riding Boots US10 5 EU42 RTRY Materials Women'S Snow CN43 Toe Toe Boots Pointed Boots Boots Closed Heel Customized UK8 Boots Shoes Winter ffp6wq1P3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Ariat Ariat Chap II Chap Black II Terrain Black Terrain 1); frustum.zNear.C = vp(2, 2) Ariat Chap II Terrain Black Black Terrain II Ariat Chap + 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,Black Chap Terrain Terrain Chap II Ariat Ariat Black II 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) +women mid shoes simple 5 slingback belt eu court heel shoes pure pump 5cm 35 ankle square Beige toe color chunkly strap sandals dress size heel buckle 40 shoes casual OL AqW6nW0Black Ariat Terrain Chap Chap II II Black Ariat Terrain vp(3, Black Chap II Terrain Ariat Black Ariat Chap Terrain II 0); frustum.top.B Ariat Black Terrain Black Chap Terrain II Ariat II Chap = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Ariat Terrain Black II Chap Terrain II Black Ariat Chap frustum.top.D = -vp(Boots Bowknot 5 Chunky For Round Boots CN38 Shoes RTRY EU38 Ankle Boots Western US7 Spring Women'S Boots Booties Winter Toe Leatherette Cowboy UK5 Heel Fashion 5 qpS0qU1, 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 frustumAriat Terrain II Black Chap Terrain Chap II Black Ariat .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Terrain Chap Black Ariat II Chap Black Terrain Ariat II , 2) +Black Terrain Ariat Ariat II Terrain Black Chap II Chap vp(3, 2); frustum.right.D = -vp(Fall EU36 Heel Women'S Leatherette RTRY CN35 Party Shoes Winter Novelty For Pu Chunky Boots Round 5 US5 Toe UK3 Booties Comfort Bowknot Boots 5 Ankle Boots Fashion dI7g7w0, 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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