Rotation example

This example explains how to use quaternions and euler angles, and how to convert between them.

Compiling and running the code

Go to gz-math/examples and use cmake to compile the code:

git clone https://github.com/gazebosim/gz-math/ -b gz-math8
cd gz-math/examples
mkdir build
cd build
cmake ..
# Linux and macOS
make
# Windows
cd ..
cmake --build build --config Release

When the code is compiled, you can run two different examples, one which converts from quaternion to euler angles:

Usage:
  ./quaternion_to_euler <float_w> <float_x> <float_y> <float_z>
 
Example
  ./quaternion_to_euler 0.5 0.5 0.5 0.5

And the other which converts from euler to quaternion:

Usage (angles specified in radians):
  quaternion_from_euler <float_roll> <float_pitch> <float_yaw>
 
Example
  quaternion_from_euler 0 0 1.57

The ouput of each program, respectively:

# Linux and macOS
./quaternion_to_euler 0.5 0.5 0.5 0.5
# Windows
.\build\Release\quaternion_to_euler.exe 0.5 0.5 0.5 0.5
Normalizing Quaternion components:
  W 0.5
  X 0.5
  Y 0.5
  Z 0.5
to
  W 0.5
  X 0.5
  Y 0.5
  Z 0.5
 
Converting to Euler angles
 roll   1.570796 radians
 pitch -0.000000 radians
 yaw    1.570796 radians
 
 roll   90.000000 degrees
 pitch -0.000000 degrees
 yaw    90.000000 degrees
 
to Rotation matrix
    0.000000   0.000000   1.000000
    1.000000   0.000000   0.000000
    0.000000   1.000000   0.000000

# Linux and macOS
./quaternion_from_euler 0 0 1.57
# Windows
.\build\Release\quaternion_from_euler.exe 0 0 1.57
Converting Euler angles:
 roll   0.000000 radians
 pitch  0.000000 radians
 yaw    1.570000 radians
 
 roll      0.000000 degrees
 pitch     0.000000 degrees
 yaw      89.954374 degrees
 
to Quaternion
 W  0.707388
 X  0.000000
 Y  0.000000
 Z  0.706825
 
to Rotation matrix
    0.000796  -1.000000   0.000000
    1.000000   0.000796   0.000000
    0.000000   0.000000   1.000000

Code

You can create some objects to express rotations:

  gz::math::Quaterniond q(roll, pitch, yaw);
  gz::math::Matrix3d m(q);

  gz::math::Vector3d euler(q.Euler());

To access the quaterions attributes:

  printf(" W % .6f\n X % .6f\n Y % .6f\n Z % .6f\n",
        q.W(), q.X(), q.Y(), q.Z());

Or to acccess the rotation matrix elements:

  std::cout << "\nto Rotation matrix\n";
  printf("   % .6f  % .6f  % .6f\n"
         "   % .6f  % .6f  % .6f\n"
         "   % .6f  % .6f  % .6f\n",
          m(0, 0), m(0, 1), m(0, 2),
          m(1, 0), m(1, 1), m(1, 2),
          m(2, 0), m(2, 1), m(2, 2));