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木虫 (著名写手)

应助: 28 (小学生)
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虫号: 1627634
注册: 2012-02-19
性别: GG
专业: 地理信息系统

[求助] 论文摘要润色【急！在线等】

三角网曲面的求交运算被广泛应用于几何造型、计算机辅助设计、GIS空间分析和三维地质建模中，基于传统计算几何的三角网曲面求交运算具有计算方式不清晰、对不同几何对象的几何运算和数学运算不统一，其向高维扩展相对较难等问题，本文引入共形几何代数理论，尝试构建不同维度、不同类型地理对象的统一表达与运算框架，进而实现多维统一的曲面求交运算及基于其上的变化检测算法。最后通过实例验证算法的有效性、准确性并进行地学解释探讨。
基于共形几何代数的多维统一分析框架，根据地理建模和应用需求，构建多维地理对象的拆分与重构，实现基于多重向量的多维统一的地理对象统一表达与存储机制。结合地理分析需求，利用所选取的代数空间所定义的基本运算规则及基本算子构造运算空间，构建面向多维空间对象计算和检索的索引机制，实现对多维对象的有效剖分、检索以及分析。
借鉴CGA多维统一的对象表达和运算结构，面向曲面求交算法的需要，实现三角面片的相交检测和求交运算，提出多维统一的三角网曲面求交运算的算法框架，构建了基于曲面求交的变化检测算法。上述算法从数学底层上统一了所涉及的不同维度的对象表达和拓扑关系运算，为地理对象的表达和模拟提供了全新的技术支撑，也为拓展多维统一的空间分析算法提供了思路。
基于南极冰盖模拟数据实现了多维统一的曲面求交运算，并基于曲面求交运算的结果，对曲面进行局部约束三角重构、变化区域提取和面积、体积等变化指标的计算，检测出南极冰盖的的变化趋势。南极冰盖案例模拟研究显示，本文构建的曲面变化检测算法具有较好的检测效果，显示基于CGA曲面求交的变化检测算法具有较好的通用性和可推广性，为高效的多维融合空间分析算法构建提供有效借鉴。

Triangulated surfaces intersection operation has been widely used in geometric modeling, computer-aided design, GIS spatial analysis and 3D geological modeling. The operation based on traditional computational geometry has some shortcomings that the method is not always intuitively clear, geometric operation and the mathematical calculation are inconsistent when deals with different geometrical objects,and it is relatively difficult to expand to the high-dimensional and so on. This thesis introduces the conformal geometric algebra theory, tries to build the framework of a unified expression and operation of different types and different dimensional geometric objects, and then implements multi-dimensional integrated structure of triangulated surfaces intersection algorithm and change detection algorithm based thereon. Finally, the accuracy, validity and geographical interpretation of mentioned algorithms are discussed through the typical case studies.
Based on the framework of conformal geometric algebra multidimensionally-unified representation and computation, ways to divide and reconstruct the multidimensional geographic objects are developed, and expressions and storage mechanism based on multivector are implemented, according to the geographical modeling and application requirements. And then, taking into account requirements of geographical spatial analysis, the thesis builds the index of the multi-dimensional space object for computing and retrieval mechanism, achieves effective division, retrieval and analysis of multi- dimensional objects using the basic operational rules defined in the algebraic space and computing space constructed by basic operators.
Referring to multidimensional unified objects expression and operation structure of conformal geometric algebra and according to the surface intersection algorithm needs, the thesis achieves the detection of triangular facets intersect and intersection computation, proposes multi-dimensional integrated structure of triangulation surface intersection algorithm framework, and based on this surface intersection algorithm, change detection algorithm is further constructed. Aforementioned algorithms unify the expression and computing of different dimensions objects, basic topology involved in the underlying of the mathematics, which provids new technogical supporting for the expression and simulation of geographical objects. The research also provdes new potential ways to extend the unified multidimensional spatial analysis methods.
Multi-dimensional Surface Intersection Algorithm is realized using Antarctic ice sheet's simulation data. And then by the results from intersection operation, we can triangle-reconstruct surface with local constraints,extract the change region,calculate the factors -area and volume,and detect Antarctic ice’s variation tendency.The Antarctic icecap’s simulation case study shows that the surface change-detection algorithm of this paper has better detection results, and that indicates the surface change detection algorithm based CGA'S Surface Intersection has good genenrality and extengding.That provides an effective reference to build a efficient,multi-dimensional integration geographic space analysis algorithm .

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