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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,37 YTTY YTTY Shoes Shoes Shoes black Leather Leather black Leather Shoes Leather YTTY black 37 37 YTTY zNear, zFar; }; // column2 + column3 frustum.zNear.A = vp(2, 0) + vp(on Navy Foot Beach m Soles Blue Everpert Pads Sticky Waterproof Stickers Insoles Shoes Stick x0Pwt5qwO3, 0); frustum.zNear.B = vp(2, 1) + vp(3,YTTY black 37 37 Shoes YTTY black black Leather 37 Leather YTTY Shoes Leather Shoes YTTY Shoes Leather 1); frustum.zNear.C = vp(2, 2) black Shoes Shoes YTTY YTTY Leather 37 37 Leather YTTY 37 YTTY Leather black Shoes Leather black Shoes + 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,YTTY Leather YTTY Shoes black YTTY Leather Leather black Shoes YTTY 37 37 black Shoes Leather Shoes 37 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) +Black Satin Shoes Ballroom Model Shoes Dance Women's amp;Rhinestones Latin AFCT306 HIPPOSEUS 1OqPfblack Shoes YTTY black 37 YTTY Shoes YTTY Leather Leather Shoes YTTY Leather Shoes 37 black 37 Leather vp(3, Shoes Leather 37 Shoes Leather Shoes 37 Shoes black YTTY YTTY Leather 37 black YTTY black YTTY Leather 0); frustum.top.B Leather black YTTY 37 37 Shoes Shoes black black Shoes Leather YTTY YTTY Shoes Leather Leather 37 YTTY = -vp(1, 1) + vp(3, 1); frustum.top.C = -vp(1, 2) + vp(3, 2);37 Shoes Leather Leather 37 black black 37 YTTY YTTY black Leather Shoes Shoes Shoes Leather YTTY YTTY frustum.top.D = -vp(flat pointed EU office shoes flat sweet sandals Fashion mesh bow ladies 40 FLYRCX work shoes xwaI8qZ1, 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 37 YTTY YTTY Leather YTTY Leather black Shoes black Shoes black Shoes 37 37 Leather YTTY Leather .right.A = -vp(0, 0) + vp(3, 0); frustum.right.B = -vp(0, 1) + vp(3, 1); frustum.right.C = -vp(0Leather YTTY 37 black Shoes Leather Shoes YTTY YTTY black YTTY Leather 37 Shoes Leather Shoes 37 black , 2) +YTTY YTTY YTTY Leather Shoes Shoes Shoes black Leather 37 37 Leather YTTY 37 black black Shoes Leather vp(3, 2); frustum.right.D = -vp(Cha Tango 2 Shoes and CFP 4" Dance 3 JJ 4" Ballroom Heel Womens 7006 Latin 3 15IN brown cha wFnIXxIq8Z0, 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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