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基于共形几何代数的GIS三维空间数据模型

, PP. 1740-1751

Keywords: 共形几何代数,三维空间数据,模型,三维度量,三维空间关系

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Abstract:

?利用共形几何代数(CGA)多维表达的统一性、几何意义的明确性及运算的坐标无关性等优势,构建了基于其上的GIS三维空间数据模型:通过建立不同维度地理对象与Clifford代数基本要素(Blades)的映射,实现代数空间中不同维度、不同类型地理对象统一表达与运算,并基于内积、外积实现了内蕴不同维度层次构建及度量关系的几何形体构建;构建了基于CGA的三维GIS空间数据模型整体架构、数据存储结构和编辑、更新机制,并基于CGA几何与拓扑运算基本算子,实现面向对象的三维GIS几何和拓扑分析功能;某小区三维数据的实例演示表明,基于CGA的三维GIS空间数据模型可有效表达不同维度的复杂几何形体,且几何和拓扑关系运算具有简明、高效等特点,具备支撑三维乃至时空GIS数据模型的潜力.

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