将四元数旋转转换为旋转矩阵？ [英] Convert Quaternion rotation to rotation matrix?

问题描述

基本上，给定quaterion（qx，qy，qz，qw）...我如何将它转换为OpenGL旋转矩阵？我也有兴趣在哪些矩阵行是向上，右，向前等...我有一个相机旋转四元数，我需要在向量中......

解决方案

以下代码基于四元数（qw，qx，qy，qz），其中的顺序基于Boost四元数：

  boost :: math :: quaternion< float>四元; 
 float qw = quaternion.R_component_1（）; 
 float qx = quaternion.R_component_2（）; 
 float qy = quaternion.R_component_3（）; 
 float qz = quaternion.R_component_4（）; 
  

首先，您必须规范化四元数：

  const float n = 1.0f / sqrt（qx * qx + qy * qy + qz * qz + qw * qw）; 
 qx * = n; 
 qy * = n; 
 qz * = n; 
 qw * = n; 
  

然后您可以创建您的矩阵：

<$ （
1.0f - 2.0f * qy * qy - 2.0f * qz * qz，2.0f * qx * qy - 2.0f * qz * qw，2.0f * qx * qz + 2.0f * qy * qw，0.0f，
2.0f * qx * qy + 2.0f * qz * qw，1.0f - 2.0f * qx * qx - 2.0f * qz * qz，2.0f * qy * qz - 2.0f * qx * qw，0.0f，
2.0f * qx * qz - 2.0f * qy * qw，2.0f * qy * qz + 2.0f * qx * qw，1.0f-2.0f * qx * qx-2.0f * qy * qy，0.0f，
0.0f，0.0f，0.0f，1.0f）;

根据您的矩阵类，您可能必须在将它传递给OpenGL之前进行转置。

Basically, given a quaterion (qx, qy, qz, qw)... How can i convert that to an OpenGL rotation matrix? I'm also interested in which matrix row is "Up", "Right", "Forward" etc... I have a camera rotation in quaternion that I need in vectors...

解决方案

The following code is based on a quaternion (qw, qx, qy, qz), where the order is based on the Boost quaternions:

boost::math::quaternion<float> quaternion;
float qw = quaternion.R_component_1();
float qx = quaternion.R_component_2();
float qy = quaternion.R_component_3();
float qz = quaternion.R_component_4();

First you have to normalize the quaternion:

const float n = 1.0f/sqrt(qx*qx+qy*qy+qz*qz+qw*qw);
qx *= n;
qy *= n;
qz *= n;
qw *= n;

Then you can create your matrix:

Matrix<float, 4>(
    1.0f - 2.0f*qy*qy - 2.0f*qz*qz, 2.0f*qx*qy - 2.0f*qz*qw, 2.0f*qx*qz + 2.0f*qy*qw, 0.0f,
    2.0f*qx*qy + 2.0f*qz*qw, 1.0f - 2.0f*qx*qx - 2.0f*qz*qz, 2.0f*qy*qz - 2.0f*qx*qw, 0.0f,
    2.0f*qx*qz - 2.0f*qy*qw, 2.0f*qy*qz + 2.0f*qx*qw, 1.0f - 2.0f*qx*qx - 2.0f*qy*qy, 0.0f,
    0.0f, 0.0f, 0.0f, 1.0f);

Depending on your matrix class, you might have to transpose it before passing it to OpenGL.

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