使用 Newell 算法计算 3d 多边形面法线的问题 [英] Issue with calculating 3d polygon's face normal using Newell's algorithm

问题描述

我正在尝试使用 Newell 的方法计算 3D 多边形的法线.我面临的问题是，即使多边形面向 -z，z 的值也总是以正数返回.但是，当它面对 -z 时，它也会翻转 x 和 y 的值，因此如果 x 的实际值为 -x，它将是 +x，y 也是如此.我不明白为什么会这样.我希望有人能指出我做错了什么.这是我到目前为止所写的内容(使用 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); $i++){//当前顶点$pi = $verticies[$i];//下一个顶点$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])));}回声 $nx.', '.$ny.', '.$nz;//当前结果 = -192.665, -145.6139, 115.1547//预期结果 = -192.665, -145.6139, -115.1547

任何帮助将不胜感激.谢谢...

解决方案

此代码 gives 0, 2, -2 为矩形

<预><代码>[[0, 0, 0],[1, 0, 0],[1, 1, 1],[0, 1, 1],];

和 0, -2, 2 用于顶点顺序颠倒的矩形，所以我认为代码是正确的

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...

解决方案

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

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