Rotation By Quaternion

最新推荐文章于 2024-07-22 20:02:46 发布

herramadeus

最新推荐文章于 2024-07-22 20:02:46 发布

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文章标签： OpenGL

本文链接：https://blog.youkuaiyun.com/herramadeus/article/details/21037211

本文详细解释了如何使用Quaternion表示三维旋转，并通过转换角度和轴向来生成旋转矩阵，适用于OpenGL环境。包括从弧度到右手坐标系的转换、单位向量标准化、角度到弧度的转换等步骤。

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P.S.: This method provides an anticlockwise positive rotation direction due to the right-handed coordinate system in OpenGL and the left-handed coordinate system in original quaternion coordinate system!

Here an assumption of a quaternion is in the form like this:
q = x*i + y*j + z*k +w;
here q is an quaternion, x, y, z, w are real and i, j, k are imaginary, which means :
pow(i, 2) == -1; pow(j, 2) == -1; pow(k, 2) == -1;

the Euler angle form rotation matrix generated with rotation angle "angR" and axis "rotAxis" via quaternion can be obtained by the following steps:
1. angR = 0.5*Pi*angR/180;    // translate angR into radian.
2. angR = - angR;    // transform to right-handed coordinate system.
3. rotAxis = normalize(rotAxis);    // normalize the axis.
4. x = rotAxis.x*sin(angR);
   y = rotAxis.y*sin(angR);
   z = rotAxis.z*sin(angR);
5. rotation matrix with homogeneous coordinates is the following matrix (for OpenGL, column-major):

6. multiple transformation matrix can be calculated by matrix multiplication normally, like
    /***************************************************/
    /*    Simp Quaternion Rotation.                */
    /***************************************************/
     CShaderProgram prog;
     CModelMatrix modelMat;
     CQuaternion quat;
     float angRX = 90.0f; float angRY = 45.0f; float angRZ = 30.0f;
     modelMat.Translatef(10.0f, 0.0f, 0.0f) ;
     modelMat.LeftMultiply(quat.GetRotationMatrix(angRX, 1, 0, 0));
     modelMat.LeftMultiply(quat.GetRotationMatrix(angRY, 0, 1, 0));
     modelMat.LeftMultiply(quat.GetRotationMatrix(angRZ, 0, 0, 1));
     prog.LoadModelMatrix(modelMat);