三角网求交的共形几何代数算法

Triangulation Intersection Algorithm Based on Conformal Geometric Algebra

针对传统三角网求交计算方法逻辑结构复杂,维度不统一等不足,基于几何代数理论,从对象表达、关系运算相统一的角度,构建了基于meet算子的自适应三角网求交算法。利用共形几何代数中与Grassmann分级结构一致的对象外积表达,建立了三角网的几何代数表达。基于meet算子构建空间三角网求交算法,探讨该算法对几何对象及维度的自适应性。最后基于南极冰盖模拟数据对上述算法进行案例验证。结果显示,本算法可以很好地支撑三角网的求交运算,在简化算法结构的同时实现了不同维度对象的自适应求交,可为基于几何代数的多维融合空间分析算法构建提供借鉴。

Traditional triangulation intersection calculation methods are insufficient in complex logical structures and not unified in dimensions. To overcome these disadvantages, an adaptive algorithm, based on the geometric algebra, is proposed. It is founded on the meet operator and from the unified object expression and relation computation perspectives. The outer product expression in Conformal Geometric Algebra, which has a property of Grassmunn structure consistency, is used for constructing the geometric algebra expression of the triangulation. The triangulation intersection algorithm is constructed based on the meet operator. The object and dimensional odaptive characteristics of this algorithm are discussed. Finally, case studies based on the Antarctic ice sheet simulation data are proposed to verify the （algorithm. The result suggests the proposed algorithm con well support the com- plex triangulation intersection operations. The algorithm structure is simplified and can be adaptive for multidimensional objects. Our research can provide a reference for the multi-dimensional unified spatial analysis methods based on geometric algebra.