四元数“规则旋转”转换为轴角时给出奇怪的值

发布于 2024-12-17 13:14:19 字数 2548 浏览 5 评论 0原文

看来我的自定义四元数实现有问题。下载我的 Java 四元数实现。

当我启动此代码片段时，为了在 Main() 方法中查看四元数角度的演变：

    Quaternion currentRotation = Quaternion.buildIdentityQuaternion();
    Quaternion constantRotation = Quaternion.buildFromAxisAngle(10, 0,1,0);

    while(true){
        float angle = currentRotation.toAxisAngle()[0];
        System.out.println(angle);
        currentRotation = constantRotation.mulInLeftOf(currentRotation);
    }

我得到以下结果：

那么为什么角度值首先变为 360 度，然后减小到 0 度？虽然我已经在 Quaternion#toAxisAngle() 方法中使用公式 2*Acos(Quaternion.w) 计算了角度？也许实现还不错，那么我如何计算角度以使其返回 0, 10, ...,350, 360, 0, 10, ..., 350, 360, 0, 10 等等？

最后，有没有办法计算真实角度？那么该角度跨越值：0,10,20,30,...,360,0,10,20...？

不过，我设法在 JOGL 程序中使用它来使简单的 6 色立方体定期旋转，只需每次计算四元数乘法并对结果四元数调用 toMatrix() 方法即可。什么有效（不关注 JOGL 具体实现细节）：

  // The OpenGL functionnalities of my program
  MyJOGLEventListener implements GLEventListener {

       Quaternion myCurrentRotation = Quaternion.buildIdentityQuaternion() // w=1, x=0, y=0, z=0
       Quaternion constantRotation = Quaternion.buildFromAxisAngle(0.02f, 0,1,0) // angle = 0.02 degrees, x=0, y=1, z=0

       GLUgl2 glu = new GLUgl2();

       public void display(GLAutoDrawable drawable) {
            GL2 gl = drawable.getGL().getGL2();
            gl.glClear(/* OMITTED : color buffer and depth buffer*/);
            gl.glLoadIdentiy();

            glu.gluLookAt(/* OMITTED */);

            /// the three most relevent lines ///////////////////////////////////
            gl.glMultMatrix(myCurrentRotation.toMatrix(), 0);

            MyCubeDrawer.drawCube(gl);

            myCurrentRotation = constantRotation.mulInLeftOf(myCurrentRotation);
            //////////////////////////////////////////////////////////////////////

      }

     // OMITED : in init(GLAutoDrawable) method, I set up depth buffer
     // OMITED : the reshape(GLAutoDrawable drawable, int x, int y, int width, int height) sets the viewport and projection
 }

问候

原文

it seems that there is a problem with my custom Quaternion implementation.
Download My quaternion implementation in Java.

When I lauch this snippet, in order to see quaternion angle evolutions, in a Main() method :

    Quaternion currentRotation = Quaternion.buildIdentityQuaternion();
    Quaternion constantRotation = Quaternion.buildFromAxisAngle(10, 0,1,0);

    while(true){
        float angle = currentRotation.toAxisAngle()[0];
        System.out.println(angle);
        currentRotation = constantRotation.mulInLeftOf(currentRotation);
    }

I've got the following results :

So why does the angle value first goes to 360 degrees then decreases toward 0 ? Though I've computed the angle with the formula 2*Acos(Quaternion.w) in Quaternion#toAxisAngle() method ? Maybe the implementation is not bad, so how can I compute the angle so that it returns 0, 10, ...,350, 360, 0, 10, ..., 350, 360, 0, 10 and so on ?

And finally, is there a way to compute the real angle ? SO that angle goes across values : 0,10,20,30,...,360,0,10,20... ?

However I managed to use it in a JOGL program to make a Simple 6-color cube rotate regularly, simply by computing a quaternion multiplication each time and by calling toMatrix() method on the result quaternion. What worked (do not pay attention to JOGL specific implementation details) :

  // The OpenGL functionnalities of my program
  MyJOGLEventListener implements GLEventListener {

       Quaternion myCurrentRotation = Quaternion.buildIdentityQuaternion() // w=1, x=0, y=0, z=0
       Quaternion constantRotation = Quaternion.buildFromAxisAngle(0.02f, 0,1,0) // angle = 0.02 degrees, x=0, y=1, z=0

       GLUgl2 glu = new GLUgl2();

       public void display(GLAutoDrawable drawable) {
            GL2 gl = drawable.getGL().getGL2();
            gl.glClear(/* OMITTED : color buffer and depth buffer*/);
            gl.glLoadIdentiy();

            glu.gluLookAt(/* OMITTED */);

            /// the three most relevent lines ///////////////////////////////////
            gl.glMultMatrix(myCurrentRotation.toMatrix(), 0);

            MyCubeDrawer.drawCube(gl);

            myCurrentRotation = constantRotation.mulInLeftOf(myCurrentRotation);
            //////////////////////////////////////////////////////////////////////

      }

     // OMITED : in init(GLAutoDrawable) method, I set up depth buffer
     // OMITED : the reshape(GLAutoDrawable drawable, int x, int y, int width, int height) sets the viewport and projection
 }

Regards

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攀登最高峰 2024-12-24 13:14:19

我怀疑你的四元数实现没问题。当您使用四元数传递 360 度时，它会反转旋转轴。因此，首先，您的四元数表示围绕正 y 轴的正旋转；然而，一旦穿过 360 度，它就开始代表绕负y轴正向旋转。

所以你得到的角度仍然是正确的。零旋转通常表示为 [1 0 0 0]。绕 y 轴旋转 180 度将表示为 [0 0 1 0]。然后旋转 360 度（显然相当于旋转 0）就是 [-1 0 0 0]。再旋转 180 度将得到 [0 0 -1 0] 这是四元数的一般属性。它们是两倍冗余。如果对四元数的所有分量取反，则相当于绕翻转轴沿相反方向旋转以获得相同的结果。

为了得到你想要的，你可以检查四元数的 y 部分。如果它小于零，则从 360 度中减去计算出的旋转，以便将轴翻转回正值。