Geometric algebra method for multidimensionally-unified GIS computation

• 来源期刊: 科学通报(英文版)
• 学科: 地球科学
• 年，卷（期）: 2012,（7）
• 页码范围: 808-817
• 页数: 10页
• 分类号: P208
• 语种: 中文

摘要

Seamless multidimensional handling and coordinate-free characteristics of geometric algebra (GA) provide means to construct multidimensionally-unified GIS computation models. Using the multivector representation for basic geometric objects within GA, we are able to construct adaptable unified geometric-topological structural models of a multidimensional geographical scene. Multidimensional operators found within the geometry, topology and GIS analysis are developed with basic GA operators. A unified computational framework is proposed, it unifies expressions and operation structures, as well as supports the analysis of multidimensional complex scenes. Finally, we illustrate modelling a three-dimensional residential district, which shows that GAbased multidimensionally-unified computation models can effectively represent and analyze complex and multidimensional geographical scenes. The development of the proposed GIS multidimensionally-unified representation, analysis, and modeling enhances current GIS algorithms and geographical models.