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

Question

I need a function that given Yaw, Pitch, and Roll, can produce the Front (or Looking At), Right, and Up vectors in "world coordinates".

In my particular world space, starting from the origin (0,0,0), X is positive to the left, Z is positive going away from the viewer/origin, and Y is positive going up.

For for example, given... (angles in degrees)

• yaw=0, pitch=0, roll=0, the expected output is:

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

• yaw=90, pitch=0, roll=0, the expected output is:

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

• yaw=0, pitch=90, roll=0, the expected output is:

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

• yaw=0, pitch=0, roll=90, the expected output is:

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

The language I'm working in is C++, and I will gladly use glm to solve this problem if that makes the most sense. If I can get there through quaternion's I'm fine with that solution as well, since I've found other tutorials that describe how to get a quaternion from euler angles.

Answer 1

Here is a full working example. It isn't very C++-like. You would probably want to use a real matrix class, but it should be ok for demonstration purposes. One thing that isn't clear from your question is the rotation order, but that can easily be changed.

#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;
}