Template-based GIS computation: a geometric algebra approach

ABSTRACT

The tight coupling between geospatial data and spatial analysis results in high costs in terms of efficiency when developing algorithms to accommodate different types of data, even when the analysis tasks are the same. Universal GIS (Geographic information system) algorithms, as alternatives to tightly coupled approaches, can reduce development costs. However, a unified representation of spatial data is necessary to support the development of universal GIS algorithms. To this end, this research proposes and implements a template-based approach using geometric algebra to create a unified representation of multidimensional data. The template is composed of parameters and operators for GIS representation and computation. The template approach can support general GIS analyses with parameter unfolding and operator integration methods. A case study of intersection analysis shows that developing programming scripts based on computation templates is much simpler than traditional methods. The results suggest that the template-based method is more efficient than traditional methods and more convenient for high-dimensional applications.

KEYWORDS:

• Geometric algebra
• computation template
• script-based programming

Acknowledgments

The National Outstanding Youth Fund (No. 41625004) and the National Natural Science Foundation of China (41601417) supported this study. The support received by A-Xing Zhu through the Vilas Associate Award, the Hammel Faculty Fellowship, the Manasse Chair Professorship from the University of Wisconsin-Madison and through the “One-Thousand Talents” Program of China is greatly appreciated.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Science Fund for Distinguished Young Scholars [41601417] and National Outstanding Youth Fund [41625004].