About OpenGA

Open-source Geometric Algebra (OpenGA) is a hub for tools and algorithms devised in light of Geometric Algebra (GA) (also known as Clifford Algebra). GA encompasses many of the standard algebraic systems used for describing geometric transformations, e.g., linear/matrix algebra, complex algebra, quaternions etc. GA-based algorithms benefit from the intrinsic mathematical generality of GA. In the core of OpenGA algorithms reside open-source libraries/toolboxes like GABLE (Geometric AlgeBra Learning Environment) and GAALET (Geometric Algebra ALgorithms Expression Templates). OpenGA is for researchers, engineers, and developers willing to apply GA in their projects.


OpenGA currently provides two applications of GA-based algorithms. The first one is adaptive filtering (one of the building blocks of machine learning and artificial intelligence); the second is 3D registration/alignment of Point Clouds. Since GA is as a lingua franca, allowing to connect different mathematical languages, we believe there are many other applications out there waiting to be reformulated from a GA perspective. OpenGA may be the starting point to achieve that.


OpenGA started with researchers working on computer vision problems. However, the capabilities of GA may be useful in other applications. We welcome the help of researchers, engineers, and developers from other areas of knowledge to improve OpenGA codes. If you are willing to contribute to this project, please contact us.