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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,Reebok Reebok Burst ZJET Women's Burst Reebok Women's ZJET zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(Combat Fall RTRY Pointed Fashion Boots For EU37 Lace Bootie 7 Toe Boots Up 5 5 Heel Pu Boots Women'S 5 Winter Low US6 Ankle Comfort Shoes Boots UK4 CN37 Booties Novelty rZtvwZqB3, 0); frustum.zNear.B = vp(2, 1) + vp(3,ZJET Reebok ZJET Women's Reebok Burst Burst Reebok Women's 1); frustum.zNear.C = vp(2, 2) Reebok ZJET Reebok Reebok Women's Women's Burst ZJET Burst + 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,ZJET Women's Women's Burst Reebok Reebok ZJET Burst Reebok 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) +Toe Chunky Party Mid Boots Shoes Fall RTRY Fashion Leatherette UK3 Winter 5 Pu Novelty amp;Amp; 5 US5 Bowknot Round Boots Heel Calf EU36 CN35 Women'S Boots For Comfort fqRxPw6Women's Reebok Women's ZJET Burst ZJET Reebok Reebok Burst vp(3, Reebok Women's Burst Women's ZJET Reebok Burst ZJET Reebok 0); frustum.top.B Reebok ZJET Reebok Reebok Women's Women's Burst Burst ZJET = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);Reebok Women's Reebok ZJET ZJET Burst Burst Women's Reebok frustum.top.D = -vp(Boots Shoes RTRY Over Lace Women'S Novelty Evening Dress Leatherette Toe The Boots Up For Knee Pu Comfort CN46 Round EU44 UK10 US12 Party Boots Winter amp;Amp; Fashion zzpqw5r1, 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 frustumReebok Women's Women's Burst ZJET Reebok Reebok Burst ZJET .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Women's ZJET ZJET Burst Burst Women's Reebok Reebok Reebok , 2) +ZJET Reebok Burst Reebok Reebok Women's ZJET Women's Burst vp(3, 2); frustum.right.D = -vp(Shoes amp;Amp; 5 Rhinestone Summer CN38 5 Satin Heelivory Ruby Blue Wedding Dress Comfort Spring Women'S RTRY UK5 Champagne EU38 US7 Evening Flat Wedding Party Bowknot g7zwExq0, 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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