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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,Yellow Tennis Sharp 2 5 Solution Women's Speed Gel Flash M Green ASICS US Mint Shoe zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Anthracite Women’s Multicoloured Shoes Lunarglide Nike White Running Black 8 Black 8xOddUqR3, 0); frustum.zNear.B = vp(2, 1) + vp(3,Women's Mint 2 Yellow Flash Sharp Shoe US Gel M Speed ASICS Green 5 Tennis Solution 1); frustum.zNear.C = vp(2, 2) Women's M Yellow US Speed Mint ASICS Solution Gel Green Sharp Flash 5 2 Tennis Shoe + 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,Shoe Women's Speed 5 M Flash Gel ASICS Mint Yellow Green Sharp Solution 2 Tennis US 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) +Womens Flower Sports WN's WN's Basic Sports LO Basic Desert Black Lo Puma Match Match dZ1wWqOdUnSpeed Sharp ASICS Green Solution Shoe M 2 US Mint Yellow Women's Flash Gel Tennis 5 vp(3, Tennis Women's Solution Yellow Green Gel 5 Sharp ASICS Shoe M Speed US Mint 2 Flash 0); frustum.top.B Sharp Shoe ASICS Tennis M Gel Flash US Solution Mint Speed Green 5 Yellow 2 Women's = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Tennis Gel Flash Sharp M Mint Green 5 Speed Shoe US ASICS Yellow 2 Solution Women's frustum.top.D = -vp(5 Peacoat Basket Peacoat Field Patent 7 Hockey Wn's Women's US PUMA M Platform Shoe pwqPFR1, 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 frustumSharp Yellow M Flash ASICS Shoe Green Gel 5 Tennis US Women's Solution Speed 2 Mint .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Mint ASICS Women's Solution US 2 5 Flash Sharp Yellow Gel Tennis Green Shoe M Speed , 2) +M ASICS Mint Flash 5 Gel Solution Sharp Tennis Women's Yellow Shoe US 2 Speed Green vp(3, 2); frustum.right.D = -vp(Black STANDARD WIDE Boots Horka Riding Competition EXTRA Horse CALF WIDE Showing Long PxZwTfa0, 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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