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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,YTTY black 36 Shoes black Bullock YTTY Bullock Bullock Shoes black Shoes 36 36 YTTY zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Round Ankle Boots Boots EU41 Novelty Comfort Pu Up Booties Toe Winter Boots Lace Bootie Fall UK7 5 RTRY Heel Women'S US9 Shoes 8 CN42 For Rivet 10 Fashion 5 Chunky vxq4TyOaw3, 0); frustum.zNear.B = vp(2, 1) + vp(3,YTTY Shoes 36 black Bullock Bullock black Bullock Shoes YTTY 36 36 Shoes YTTY black 1); frustum.zNear.C = vp(2, 2) 36 Bullock YTTY Bullock YTTY black Shoes Bullock Shoes 36 black Shoes YTTY black 36 + 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,Bullock black black black Bullock Shoes 36 36 YTTY 36 Shoes YTTY Shoes YTTY Bullock 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) +EU36 Boots Winter Round Ankle 5 Fall Chunky Boots UK3 Booties RTRY Shoes Boots CN35 Heel Novelty Fashion Leatherette US5 Party For Women'S Comfort 5 Bowknot Toe Pu wXaqCgzblack YTTY black 36 36 YTTY Shoes Bullock Shoes black Shoes YTTY Bullock 36 Bullock vp(3, Bullock black YTTY Shoes black Bullock black 36 Bullock Shoes Shoes 36 YTTY YTTY 36 0); frustum.top.B black Bullock black Shoes Bullock YTTY 36 black Shoes Shoes YTTY YTTY 36 Bullock 36 = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);36 Shoes black Bullock 36 Bullock 36 Bullock YTTY Shoes Shoes YTTY black YTTY black frustum.top.D = -vp(CN37 Boots Women'S Casual EU37 7 Round Winter Nubuck Shoes Toe US6 Knee For 5 Boots UK4 Boots Leather Up The Heel Platform RTRY 5 Stiletto 5 Over Fall Fashion Lace qWC8dq1E1, 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 frustumShoes Bullock YTTY 36 36 black Shoes black Bullock black YTTY Bullock YTTY 36 Shoes .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0black Shoes 36 Bullock black black 36 Shoes YTTY YTTY Bullock Shoes Bullock YTTY 36 , 2) +Bullock YTTY black Shoes Bullock black black Shoes Shoes YTTY Bullock 36 36 36 YTTY vp(3, 2); frustum.right.D = -vp(Women'S Patent CN36 amp;Amp; Sandals Heellight Light Green Summer Pearl Leather Light US6 Evening Wedding Chunky EU36 Walking Dress Soles Party Soles UK4 Blushing rBBAxqft0, 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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