如何将欧拉角转换为前，上，右矢量

How to convert Euler Angles to Front, Up, Right vectors

本文关键字：转换      更新时间：2023-10-16

我需要一个函数，给定偏航，俯仰和滚动，可以在"世界坐标"中产生前(或看)，右和向上向量。

在我的特定世界空间中，从原点(0,0,0)开始，X为正向左，Z为正远离观察者/原点，Y为正向上。

例如，给定…(角度单位:度)

  • 偏航=0，俯仰=0，横摇=0，预期输出为:

    • front = (0.0,0.0,1.0)
    • right = (-1.0,0.0,0.0)
    • up = (0.0,1.0,0.0)

  • 偏航=90，俯仰=0，横摇=0，预期输出为:

    • front = (1.0,0.0,0.0)
    • right = (0,0,0.0,1.0)
    • up = (0.0,1.0,0.0)

  • 偏航=0，俯仰=90，横摇=0，预期输出为:

    • front = (0.0,1.0,0.0)
    • right = (-1.0,0.0,0.0)
    • up = (0.0,0.0，-1.0)

  • 偏航=0，俯仰=0，横摇=90，预期输出为:

    • front = (0.0,0.0,1.0)
    • right = (0.0,1.0,0.0)
    • up = (1.0,0.0,0.0)

我正在使用的语言是c++，如果最有意义的话，我很乐意使用glm来解决这个问题。如果我能通过四元数得到它，我对这个解决方案也很满意，因为我已经找到了其他教程，描述了如何从欧拉角度得到四元数。

下面是一个完整的工作示例。它不是很像c++。您可能希望使用一个真正的矩阵类，但出于演示目的，它应该是可以的。从你的问题中有一点不清楚，那就是旋转顺序，但这很容易改变。

#include <iostream>
#include <cmath>
#include <cstdlib>
typedef float Float;
typedef Float Axis[3];
typedef Axis Axes[3];
static void copy(const Axes &from,Axes &to)
{
  for (size_t i=0; i!=3; ++i) {
    for (size_t j=0; j!=3; ++j) {
      to[i][j] = from[i][j];
    }
  }
}
static void mul(Axes &mat,Axes &b)
{
  Axes result;
  for (size_t i=0; i!=3; ++i) {
    for (size_t j=0; j!=3; ++j) {
      Float sum = 0;
      for (size_t k=0; k!=3; ++k) {
        sum += mat[i][k]*b[k][j];
      }
      result[i][j] = sum;
    }
  }
  copy(result,mat);
}
static void getAxes(Axes &result,Float yaw,Float pitch,Float roll)
{
  Float x = -pitch;
  Float y = yaw;
  Float z = -roll;
  Axes matX = {
    {1,     0,     0 },
    {0, cos(x),sin(x)},
    {0,-sin(x),cos(x)}
  };
  Axes matY = {
    {cos(y),0,-sin(y)},
    {     0,1,      0},
    {sin(y),0, cos(y)}
  };
  Axes matZ = {
    { cos(z),sin(z),0},
    {-sin(z),cos(z),0},
    {      0,     0,1}
  };
  Axes axes = {
    {1,0,0},
    {0,1,0},
    {0,0,1}
  };
  mul(axes,matX);
  mul(axes,matY);
  mul(axes,matZ);
  copy(axes,result);
}

static void showAxis(const char *desc,const Axis &axis,Float sign)
{
  std::cout << "  " << desc << " = (";
  for (size_t i=0; i!=3; ++i) {
    if (i!=0) {
      std::cout << ",";
    }
    std::cout << axis[i]*sign;
  }
  std::cout << ")n";
}
static void showAxes(const char *desc,Axes &axes)
{
  std::cout << desc << ":n";
  showAxis("front",axes[2],1);
  showAxis("right",axes[0],-1);
  showAxis("up",axes[1],1);
}
int main(int,char**)
{
  Axes axes;
  std::cout.setf(std::ios::fixed);
  std::cout.precision(1);
  getAxes(axes,0,0,0);
  showAxes("yaw=0, pitch=0, roll=0",axes);
  getAxes(axes,M_PI/2,0,0);
  showAxes("yaw=90, pitch=0, roll=0",axes);
  getAxes(axes,0,M_PI/2,0);
  showAxes("yaw=0, pitch=90, roll=0",axes);
  getAxes(axes,0,0,M_PI/2);
  showAxes("yaw=0, pitch=0, roll=90",axes);
  return 0;
}
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