关键词: 共形几何代数, 三角网表达, 三角网求交, meet算子, 空间关系判断

Abstract:

Traditional triangular mesh 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 in this paper. 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 Grassmann structure consistency, is used for constructing the geometric algebra expression of the triangular mesh. The triangular intersection algorithm is constructed based on the meet operator. The object and dimensional adaptive characteristics of this algorithm is discussed. Finally, case studies based on the Antarctic ice sheet simulation data are proposed to verify the algorithm. The result suggests the proposed algorithm can well support the complex triangle mesh intersection operations, and simplify the algorithm structures and enhance the multidimensional applicability. Our research can provide a reference for the multi-dimensional unified spatial analysis methods based on geometric algebra.

Key words: Conformal geometric algebra, triangulation network expression, triangulation network intersection, meet operator, spatial relation judgment