Question

我正在使用lib glm（http://glm.g-truc.net/）来测试四元数，但我遇到了问题;当我将欧拉角转换为四元数然后立即将四元数转换为欧拉角时，我的结果与我的初始欧拉角完全不同。这是正常的吗？可能是因为轮换不是交际的？

代码测试：

#include <glm\quaternion.hpp>
#include <math.h>

#define PI M_PI
#define RADTODEG(x) ( (x) * 180.0 / PI )
#define DEGTORAD(x) ( (x) * PI / 180.0 )

int         main( void )
{
    float RotX = 90.f;
    float RotY = 180.f;
    float RotZ = -270.f;

    if ( RotX || RotY || RotZ )
    {
        std::cout << "Init: x= " << RotX << ", y= " << RotY << ", z= " << RotZ << "\n";
        glm::quat key_quat(glm::detail::tvec3<float>(DEGTORAD( RotX ),
                                                     DEGTORAD( RotY ),
                                                     DEGTORAD( RotZ )));
        glm::detail::tvec3<float> v = glm::eulerAngles(key_quat);

        /*  // the result is even worse with this code here
        RotX = RADTODEG(v.x);
        RotY = RADTODEG(v.y);
        RotZ = RADTODEG(v.z);
        */

        RotX = v.x;
        RotY = v.y;
        RotZ = v.z;

        std::cout << "Final: x= " << RotX << ", y= " << RotY << ", z= " << RotZ << "\n";
    }
    return (0);
}

结果：

Init: x= 90, y= 180, z= -270
Final: x= -90, y= -3.41509e-006, z= -90

提前谢谢o /

Answer 1

是的，这很正常。 There are 2 ways用欧拉角表示相同的旋转。

我个人不喜欢欧拉角，they mess up the stability of your app.我会避开它们。另外，它们也是not very handy。

Answer 2

看一下这个页面。它拥有您需要的一切（甚至一些代码示例！）来处理3D转换。

Quaternion to Euler Angles

Euler Angles to Quaternion

All rotation conversions

Answer 3

如果你最终需要四元数到欧拉角，但你需要一个任意的旋转顺序，我遇到了一个带有转换代码的网站。有时诀窍就是找到正确的旋转顺序。（顺便说一句，具有相同字母两次的订单，如XYX，是正确的欧拉角，但像XYZ的那些是Tait-Bryan角）。

以下是链接：http://bediyap.com/programming/convert-quaternion-to-euler-rotations/

这是代码：

///////////////////////////////
// Quaternion to Euler
///////////////////////////////
enum RotSeq{zyx, zyz, zxy, zxz, yxz, yxy, yzx, yzy, xyz, xyx, xzy,xzx};

void twoaxisrot(double r11, double r12, double r21, double r31, double r32, double res[]){
  res[0] = atan2( r11, r12 );
  res[1] = acos ( r21 );
  res[2] = atan2( r31, r32 );
}

void threeaxisrot(double r11, double r12, double r21, double r31, double r32, double res[]){
  res[0] = atan2( r31, r32 );
  res[1] = asin ( r21 );
  res[2] = atan2( r11, r12 );
}

void quaternion2Euler(const Quaternion& q, double res[], RotSeq rotSeq)
{
    switch(rotSeq){
    case zyx:
      threeaxisrot( 2*(q.x*q.y + q.w*q.z),
                     q.w*q.w + q.x*q.x - q.y*q.y - q.z*q.z,
                    -2*(q.x*q.z - q.w*q.y),
                     2*(q.y*q.z + q.w*q.x),
                     q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z,
                     res);
      break;

    case zyz:
      twoaxisrot( 2*(q.y*q.z - q.w*q.x),
                   2*(q.x*q.z + q.w*q.y),
                   q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z,
                   2*(q.y*q.z + q.w*q.x),
                  -2*(q.x*q.z - q.w*q.y),
                  res);
      break;

    case zxy:
      threeaxisrot( -2*(q.x*q.y - q.w*q.z),
                      q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z,
                      2*(q.y*q.z + q.w*q.x),
                     -2*(q.x*q.z - q.w*q.y),
                      q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z,
                      res);
      break;

    case zxz:
      twoaxisrot( 2*(q.x*q.z + q.w*q.y),
                  -2*(q.y*q.z - q.w*q.x),
                   q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z,
                   2*(q.x*q.z - q.w*q.y),
                   2*(q.y*q.z + q.w*q.x),
                   res);
      break;

    case yxz:
      threeaxisrot( 2*(q.x*q.z + q.w*q.y),
                     q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z,
                    -2*(q.y*q.z - q.w*q.x),
                     2*(q.x*q.y + q.w*q.z),
                     q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z,
                     res);
      break;

    case yxy:
      twoaxisrot( 2*(q.x*q.y - q.w*q.z),
                   2*(q.y*q.z + q.w*q.x),
                   q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z,
                   2*(q.x*q.y + q.w*q.z),
                  -2*(q.y*q.z - q.w*q.x),
                  res);
      break;

    case yzx:
      threeaxisrot( -2*(q.x*q.z - q.w*q.y),
                      q.w*q.w + q.x*q.x - q.y*q.y - q.z*q.z,
                      2*(q.x*q.y + q.w*q.z),
                     -2*(q.y*q.z - q.w*q.x),
                      q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z,
                      res);
      break;

    case yzy:
      twoaxisrot( 2*(q.y*q.z + q.w*q.x),
                  -2*(q.x*q.y - q.w*q.z),
                   q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z,
                   2*(q.y*q.z - q.w*q.x),
                   2*(q.x*q.y + q.w*q.z),
                   res);
      break;

    case xyz:
      threeaxisrot( -2*(q.y*q.z - q.w*q.x),
                    q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z,
                    2*(q.x*q.z + q.w*q.y),
                   -2*(q.x*q.y - q.w*q.z),
                    q.w*q.w + q.x*q.x - q.y*q.y - q.z*q.z,
                    res);
      break;

    case xyx:
      twoaxisrot( 2*(q.x*q.y + q.w*q.z),
                  -2*(q.x*q.z - q.w*q.y),
                   q.w*q.w + q.x*q.x - q.y*q.y - q.z*q.z,
                   2*(q.x*q.y - q.w*q.z),
                   2*(q.x*q.z + q.w*q.y),
                   res);
      break;

    case xzy:
      threeaxisrot( 2*(q.y*q.z + q.w*q.x),
                     q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z,
                    -2*(q.x*q.y - q.w*q.z),
                     2*(q.x*q.z + q.w*q.y),
                     q.w*q.w + q.x*q.x - q.y*q.y - q.z*q.z,
                     res);
      break;

    case xzx:
      twoaxisrot( 2*(q.x*q.z - q.w*q.y),
                   2*(q.x*q.y + q.w*q.z),
                   q.w*q.w + q.x*q.x - q.y*q.y - q.z*q.z,
                   2*(q.x*q.z + q.w*q.y),
                  -2*(q.x*q.y - q.w*q.z),
                  res);
      break;
    default:
      std::cout << "Unknown rotation sequence" << std::endl;
      break;
   }
}

Answer 4

Euler - ＆gt;四元数

从Three.js中提取。

这是一段适合我的代码：

function eulerToQuaternion(eulerXYZ) {
  var c1 = Math.cos(eulerXYZ[0] / 2),
    c2 = Math.cos(eulerXYZ[1] / 2),
    c3 = Math.cos(eulerXYZ[2] / 2),
    s1 = Math.sin(eulerXYZ[0] / 2),
    s2 = Math.sin(eulerXYZ[1] / 2),
    s3 = Math.sin(eulerXYZ[2] / 2),
    x = s1 * c2 * c3 + c1 * s2 * s3,
    y = c1 * s2 * c3 - s1 * c2 * s3,
    z = c1 * c2 * s3 + s1 * s2 * c3,
    w = c1 * c2 * c3 - s1 * s2 * s3;

  return [x, y, z, w];
};

function calculate() {
  var quat = eulerToQuaternion([document.querySelector('#x').value, document.querySelector('#y').value, document.querySelector('#z').value]);

  document.querySelector('#result').innerHTML = quat.join(' &nbsp; ');
}

<h3>Euler radians in XYZ order:</h3>
<fieldset>
  <label>X:
    <input id="x" value="1.5" />
  </label>
  <label>Y:
    <input id="y" value="1" />
  </label>
  <label>Z:
    <input id="z" value="0" />
  </label>
  <button onClick="calculate()">To Quaternion</button>
</fieldset>
<h3>X Y Z W result:</h3>
<div id="result"></div>

欧拉角到四元数然后四元数到欧拉角

4 个答案: