Issue with calculating 3d polygon's face normal using Newell's algorithm

问题

I'm trying to calculate 3D polygon's normal using Newell's approach. The problem I'm facing is that the value of z is always returned in positive even though the polygon is facing -z. However, when it's facing -z it also flips the values of x and y as well so if actual value of x is -x it'll be +x and same goes for the y. I can't figure out why that is happening. I hope someone can point out what I'm doing wrong. Here's what I wrote so far (using PHP):

$verticies =
[
    [57.36, 30.98, 0.0],
    [52.57, 39.04, 2.76],
    [58.00, 38.33, 10.50],
    [59.89, 31.16, 4.77],
    [62.28, 30.75, 8.01],
    [64.70, 26.11, 6.46],
    [64.90, 21.54, 1.21]
];

for ($i = 0; $i < count($verticies); $i++) 
{
    //current vertex
    $pi = $verticies[$i];

    //next vertex
    $pj = $verticies[($i+1) % count($verticies)];

    //0 = x, 1 = y, 2 = z
    $nx += ((($pi[2]) + ($pj[2])) * (($pj[1]) - ($pi[1])));
    $ny += ((($pi[0]) + ($pj[0])) * (($pj[2]) - ($pi[2])));
    $nz += ((($pi[1]) + ($pj[1])) * (($pj[0]) - ($pi[0])));
}

echo $nx.', '.$ny.', '.$nz;

//Current Result = -192.665, -145.6139, 115.1547
//Expected Result = -192.665, -145.6139, -115.1547

Any help would be appreciated. Thanks...

回答1:

This code gives 0, 2, -2 for rectangle

[
    [0, 0, 0],
    [1, 0, 0],
    [1, 1, 1],
    [0, 1, 1],
];

and 0, -2, 2 for rectangle with reversed vertex order, so I think code is right

来源：https://stackoverflow.com/questions/59124545/issue-with-calculating-3d-polygons-face-normal-using-newells-algorithm

标签

php

algorithm

geometry

polygon