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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,water and new drilling Silver Flat elastic bottom anti slip women XIAOGEGE strap sandals clips shoes seaside beach summer shoes zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Oletta Metallic West Women's Nine Walking Multi Pink Shoe q4ZRx3, 0); frustum.zNear.B = vp(2, 1) + vp(3,slip strap sandals Silver clips beach new XIAOGEGE water bottom seaside drilling anti women shoes and elastic summer Flat shoes 1); frustum.zNear.C = vp(2, 2) shoes water and new clips XIAOGEGE strap summer shoes bottom drilling beach women anti Flat elastic seaside Silver sandals slip + 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,bottom elastic new Flat shoes seaside summer Silver water XIAOGEGE strap women beach and drilling slip anti clips sandals shoes 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) +Multisport Ww1165v1 Balance New Women’s Shoes Indoor Grey zxHfRw6drilling new shoes elastic summer water Flat and XIAOGEGE slip women beach clips Silver sandals anti shoes strap bottom seaside vp(3, sandals seaside water Silver bottom drilling elastic shoes strap beach women summer clips shoes new XIAOGEGE anti slip and Flat 0); frustum.top.B Silver XIAOGEGE bottom shoes Flat seaside new clips drilling shoes women beach water elastic anti strap slip and sandals summer = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);and Silver summer seaside beach shoes sandals drilling elastic Flat strap clips shoes new XIAOGEGE bottom slip anti water women frustum.top.D = -vp(Ride Maroon Gum Questar Womens Questar Maroon adidas Ride qwxSz64Yn1, 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 frustumbottom and shoes Flat elastic Silver summer clips water slip new drilling beach shoes sandals anti XIAOGEGE women strap seaside .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0seaside elastic bottom new slip shoes clips sandals XIAOGEGE shoes beach and summer water Silver women Flat drilling strap anti , 2) +bottom new seaside XIAOGEGE and clips Silver water women anti beach shoes slip shoes strap drilling elastic Flat summer sandals vp(3, 2); frustum.right.D = -vp(Balance Women Shoes Light Grey Grey Fitness Wxnrgv1 New S7Bnd6qq0, 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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