通给给定旋转轴向量v，旋转角度ang，计算出旋转矩阵

chai3d中通过计算旋转轴和角度来获得旋转矩阵Matrix3

 inline bool rotateAboutLocalAxisRad(const cVector3d& a_axis,
                                      const double& a_angleRad)
  {
      // compute length of axis vector
      double length = a_axis.length();


      // check length of axis vector
      if (length < C_TINY)
      {
          // rotation matrix could not be computed because axis vector is not defined
          return (false);
      }


      // normalize axis vector
      double f = 1.0 / length;
      double x = f * a_axis(0);
      double y = f * a_axis(1);
      double z = f * a_axis(2);


      // compute rotation matrix
      double c = ::cos(a_angleRad);
      double s = ::sin(a_angleRad);
      double v = 1-c;


      cMatrix3d m;
      m(0,0) = x*x*v+c;     m(0,1) = x*y*v-z*s;  m(0,2) = x*z*v+y*s;
      m(1,0) = x*y*v+z*s;   m(1,1) = y*y*v+c;    m(1,2) = y*z*v-x*s;
      m(2,0) = x*z*v-y*s;   m(2,1) = y*z*v+x*s;  m(2,2) = z*z*v+c;


      (*this) = (*this)*m;


      // return success
      return (true);
  }

上面的函数中的绕任意轴旋转获得的旋转矩阵的算法实现思路如下：

根据Goldman给出的公式进行计算，这个公式有点复杂：

具体推导过程可以参考：

http://www.cppblog.com/lovedday/archive/2008/01/12/41031.html

http://www.cnblogs.com/cg_ghost/archive/2012/04/27/2473347.html