tinyso3

TinySO3 is a compact and efficient library designed to handle 3D rotations using various mathematical representations including rotation matrices, quaternions, and Lie groups (SO(3)). Whether you're working on robotics, computer graphics, or aerospace applications, TinySO3 provides the essential tools for managing and manipulating 3D rotational data with precision and ease.

Theory document

Features

• Rotation Matrices: Functions for creating, transforming, and composing rotation matrices.
  • Supported Convention : Passive(Alias) and Active(Alibi)
• Quaternions: Comprehensive support for quaternion algebra, including conversion, interpolation, and normalization.
  • Supported Convention : Hamilton and JPL
• Axis Angle: Tools for representing and converting rotations using the axis-angle representation.
• Euler Angles: Support for multiple Euler angle conventions and conversion between Euler angles and other representations.
  • Supported Convention : Intrinsic and Extrinsic
  • All 12 representation of euler angles are supported, including Tait-Bryan and Proper.
• Lie Groups: Efficient methods for working with Lie group representations of rotations, specifically SO(3).
• Interoperability: Seamless conversion between different rotation representations.
• Conversion between Euler Rate and Angular Velocity
• Performance: Optimized for speed and minimal memory usage, making it suitable for real-time applications.
• C++11 Header-Only library.
• Standard C++ library is not required.
• No dynamic allocations.

Installation

tinyso3 has no dependencies except testing(disabled by default).

tinyso3 follows general steps of CMake projects.

Before installation, you can configure default template arguments.

pip install kconfiglib
make config

Or manually configure config.hpp, version.hpp

Option 1 (CMake)

mkdir -p build && cd build
cmake .. -DCMAKE_BUILD_TYPE=Release
cmake --build . -- -j
cmake --install .

find_package(tinyso3 REQUIRED)
add_executable(myapp main.cpp)
target_link_library(myapp PRIVATE tinyso3::tinyso3)

Option 2 (CMake FetchContents)

include(FetchContent)
FetchContent_Declare(tinyso3 GIT_REPOSITORY
https://github.com/timetravelCat/tinyso3)
FetchContent_MakeAvailable(tinyso3)
...
target_link_libraries(myapp PRIVATE tinyso3)

Option 3 (Copy & Paste)

Copy include/tinyso3 folder to your project. C++11 compiler is required.

Tutorials

See the test directory for detailed examples.

tutorial.cpp

/**
 * @file tutorial.cpp
 * 
 * A simple tutorial for TinySO(3).
 */
#include <tinyso3/tinyso3.hpp>

using namespace tinyso3;

int main(int argc, char const* argv[]) {
    /**
     * Basic Matrix and Vector operations
     */
    float matrix_43_data[4][3] = {
      {01.f, 02.f, 03.f},
      {04.f, 05.f, 06.f},
      {07.f, 08.f, 09.f},
      {10.f, 11.f, 12.f}};

    float matrix_34_data[3][4] = {
      {01.f, 02.f, 03.f, 04.f},
      {05.f, 06.f, 07.f, 08.f},
      {09.f, 10.f, 11.f, 12.f}};

    Matrix<4, 3, float> matrix_43(matrix_43_data);
    Matrix<3, 4, float> matrix_34(matrix_34_data);

    SquareMatrix<4, float> matrix_44 = matrix_43 * matrix_34;
    Vector<4, float> vector_4 = matrix_44.slice<4, 1>(0, 2);
    Vector3<float> vector3 = vector_4.slice<3, 1>(1, 0);
    vector3 -= SquareMatrix<3, float>::Identity().diag() * 2.f;
    vector3.normalize();
    vector3 = vector3.hat().vee();

    /**
     * 3D Rotation Representations
     */
    Euler<INTRINSIC, ZYX, float> euler{0.1f, 0.2f, 0.3f};
    Quaternion<HAMILTON, float> quaternion = euler;
    AxisAngle<float> axis_angle = quaternion;
    RotationMatrix<ACTIVE, float> rotation_matrix = axis_angle;

    /**
     * Rotate vectors
     */
    vector3 = rotation_matrix * vector3;
    vector3 = quaternion * vector3;

    /**
     * Normalize quaternion or rotation matrix
     */
    quaternion.normalize();
    rotation_matrix.normalize();

    /**
     * Interpolation between two rotations
     */
    Euler<INTRINSIC, ZYX, float> euler_compare{0.2f, 0.3f, 0.4f};
    Quaternion<HAMILTON, float> quaternion_compare = euler_compare;
    Quaternion<HAMILTON, float> quaternion_interpolated = quaternion.slerp(quaternion_compare, 0.5f);
    RotationMatrix<ACTIVE, float> rotation_matrix_compare = euler_compare;
    RotationMatrix<ACTIVE, float> rotation_matrix_interpolated = rotation_matrix.interpolate(rotation_matrix_compare, 0.5f);

    /**
     * Conversion between angular velocity and Euler rate
     */
    AngularVelocity<float> angular_velocity(Vector3<float>{0.1f, 0.2f, 0.3f});
    EulerRate<INTRINSIC, ZYX, float> euler_rate = angular_velocity;
    angular_velocity = euler_rate;

    return 0;
}

Development

Running the tests

• Install Catch2 v3.4 or higher

mkdir -p build && cd build
cmake .. -DBUILD_TESTING=ON
cmake --build . -- -j
ctest # or make test

Formatting

• Install clang-format and cmake-format

pip install cmake-format
sudo apt install clang-format 

make format # all c++ files and cmake files will be formatted.

• If you are using vscode, install clang-format extension.

Static Analyzers

sudo apt install cppcheck clang-tidy

Documentations

pip3 install mkdocs mkdocs-material pymdown-extensions mkdocs-dracula-theme 
mkdocs build
mkdocs serve

License

This project is licensed under the BSD-3-Clause - see the LICENSE file for details

Contact

timetravelCat - timetraveler930@gmail.com

Contributors

Special thanks to @lightAxis who implemented the quaternion functionality.