围绕其中心点/轴旋转 3D 形状

问题描述

我在 STL 文件中定义了一个 3D 形状，我想使用 Yaw、Pitch 和 Roll 围绕它的轴/中心旋转它.但是，我已经实现了一个解决方案，但它并没有按预期工作，因为 它会围绕原点轴旋转 3D 形状.这是我到目前为止所做的(用 PHP 编写):

I have a 3D shape defined in STL file and I'd like to rotate it around its axis/center using Yaw, Pitch and Roll. However, I've already implemented a solution and it doesn't work as expected as it rotates the 3D shape around the origin axis instead. Here's what I've done so far (written in PHP):

function rotate($vertices, $roll = 0, $pitch = 0, $yaw = 0) 
{
    if(!empty($vertices))
    {
        $cosa = cos($yaw);
        $sina = sin($yaw);

        $cosb = cos($pitch);
        $sinb = sin($pitch);

        $cosc = cos($roll);
        $sinc = sin($roll);

        $Axx = $cosa * $cosb;
        $Axy = $cosa * $sinb * $sinc - $sina * $cosc;
        $Axz = $cosa * $sinb * $cosc + $sina * $sinc;

        $Ayx = $sina * $cosb;
        $Ayy = $sina * $sinb * $sinc + $cosa * $cosc;
        $Ayz = $sina * $sinb * $cosc - $cosa * $sinc;

        $Azx = -$sinb;
        $Azy = $cosb * $sinc;
        $Azz = $cosb * $cosc;

        //loop through all triangles
        foreach($vertices as $i => $vertex) 
        {
            $px = $vertex->x;
            $py = $vertex->y;
            $pz = $vertex->z;

            $points = 
            [
                'x' => ($Axx * $px + $Axy * $py + $Axz * $pz), 
                'y' => ($Ayx * $px + $Ayy * $py + $Ayz * $pz), 
                'z' => ($Azx * $px + $Azy * $py + $Azz * $pz)
            ];

            //update the vertex
            $vertices[$i]->setVertex($vi, $points);
        }
    }

    return $vertices;
}

如果我遗漏了什么，请告诉我.任何帮助将不胜感激.

Please let me know if I'm missing something. any help would be appreciated.

推荐答案

上面的代码绕原点旋转.如果您的旋转中心(例如 $c)不是原点，您可以在旋转之前移动对象:

The code above rotates about the origin. If your centre of rotation (say, $c), isn't the origin, you can move the object before rotating:

$px = $vertex->x - $c->x;
$py = $vertex->y - $c->y;
$pz = $vertex->z - $c->z;

旋转后，将点移回旋转中心:

After rotating, move the point back to the centre of rotation:

$points = 
[
    'x' => ($Axx * $px + $Axy * $py + $Axz * $pz) + $c->x, 
    'y' => ($Ayx * $px + $Ayy * $py + $Ayz * $pz) + $c->y, 
    'z' => ($Azx * $px + $Azy * $py + $Azz * $pz) + $c->z
];

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