围绕其 centeroid/axis 旋转 3D 形状

Question

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 axis/center 旋转它。但是，我已经实施了一个解决方案，但它并没有像预期的那样工作，因为 它绕原点轴旋转 3D 形状而不是 。这是我到目前为止所做的（写在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。

Answer 1

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：

$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：

$points = 
[
    'x' => ($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
];

围绕其 centeroid/axis 旋转 3D 形状

Rotate 3D shape around its centeroid/axis

php

3d

geometry

rotation