本文選題：幾何代數(shù) + 時空拓撲關(guān)系計算　； 參考：《浙江大學(xué)學(xué)報(理學(xué)版)》2017年01期

【摘要】：根據(jù)幾何代數(shù)在地理空間對象建模和多維數(shù)據(jù)分析應(yīng)用的特點,研究了共形幾何代數(shù)交/并(meet/join)算子的含義、構(gòu)建和應(yīng)用.利用幾何代數(shù)多維統(tǒng)一、高維計算適應(yīng)的優(yōu)勢,設(shè)計了基于幾何代數(shù)meet算子和有向半空間劃分理論的時空宗地meet算法.從三維地籍和時空數(shù)據(jù)建模出發(fā),在共形幾何代數(shù)和時空代數(shù)范疇中,給出了三維、四維時空宗地的定義和表達.同時,以宗地數(shù)據(jù)的拓撲計算為例,將該算法運用于三維時空宗地拓撲計算場景——歷史回溯中,取得了良好的效果.該算法的理念同樣適用于四維時空宗地的歷史回溯meet求解.
[Abstract]:According to the characteristics of geometric algebra in geo-spatial object modeling and multidimensional data analysis, the meaning, construction and application of conformal geometric algebra intersection / parallel meet-join operator are studied. Based on the advantages of multi-dimensional unification of geometric algebra and adaptability of high-dimensional computation, a spatio-temporal meet algorithm based on geometric algebra meet operator and directed midspace partition theory is designed. Based on the modeling of three-dimensional cadastral and space-time data, the definition and expression of three-dimensional and four-dimensional space-time land are given in the category of conformal geometric algebra and space-time algebra. At the same time, taking the topological calculation of the land data as an example, the algorithm is applied to the scene of 3D temporal and spatial land topology calculation-historical backtracking, and good results are obtained. The idea of this algorithm is also applicable to the historical backtracking meet solution of four dimensional temporal and spatial land.
【作者單位】： 浙江大學(xué)浙江省資源與環(huán)境信息系統(tǒng)重點實驗室;浙江大學(xué)地球科學(xué)學(xué)院;
【基金】：國家自然科學(xué)基金資助項目(41471313,41101356,41101371,41171321) 國家科技基礎(chǔ)性工作專項(2012FY112300) 海洋公益性行業(yè)科研專項經(jīng)費資助(2015418003,201305012) 浙江省攻關(guān)項目(2014C33G20,2013C33051)
【分類號】：P208
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本文編號：1861040