在一个轴上旋转一个四元数？ [英] rotating a quaternion on 1 axis?

问题描述

我有一个由四元数旋转的模型。我只能设置旋转，我不能从任何东西中加或减。我需要得到一个轴的值​​，并添加一个角度（可能是度数或弧度？），然后重新添加修改的四元数。

我可以这样做吗？ （在每个轴上的答案）。

解决方案

您可以将两个四元数相乘以产生第三个四元数，旋转。请注意，四元数乘法不是可交换的，这意味着顺序很重要（如果你在脑子里做了几次，你可以看到为什么）。

你可以生成一个四元数代表一个围绕特定轴的给定角度的旋转，像这样的东西（原谅它是c ++，而不是java）：

  Quaternion Quaternion :: create_from_axis_angle（const double& xx，const double& yy，const double& zz，const double& a）
 {
 //这里我们计算sin（theta / 2）一次优化
 double factor = sin（a / 2.0）; 
 
 //计算四元数的x，y和z 
 double x = xx * factor; 
 double y = yy * factor; 
 double z = zz * factor; 
 
 //通过cos（theta / 2）计算w值w 
 double w = cos（a / 2.0）; 
 
返回Quaternion（x，y，z，w）.normalize（）; 
 
 $ / code> 

例如，要围绕x轴旋转，可以创建一个四元数 createFromAxisAngle（1,0,0，M_PI / 2）并将其乘以模型的当前四元数。


I have a model rotated by a quaternion. I can only set the rotation, I can't add or subtract from anything. I need to get the value of an axis, and than add an angle to it (maybe a degree or radian?) and than re-add the modified quaternion.

How can I do this? (answer on each axis).

解决方案

You can multiply two quaternions together to produce a third quaternion that is the result of the two rotations. Note that quaternion multiplication is not commutative, meaning order matters (if you do this in your head a few times, you can see why).

You can produce a quaternion that represents a rotation by a given angle around a particular axis with something like this (excuse the fact that it is c++, not java):

Quaternion Quaternion::create_from_axis_angle(const double &xx, const double &yy, const double &zz, const double &a)
{
    // Here we calculate the sin( theta / 2) once for optimization
    double factor = sin( a / 2.0 );

    // Calculate the x, y and z of the quaternion
    double x = xx * factor;
    double y = yy * factor;
    double z = zz * factor;

    // Calcualte the w value by cos( theta / 2 )
    double w = cos( a / 2.0 );

    return Quaternion(x, y, z, w).normalize();
}

So to rotate around the x axis for example, you could create a quaternion with createFromAxisAngle(1, 0, 0, M_PI/2) and multiply it by the current rotation quaternion of your model.

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