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Making direction a first-class citizen of Tobler's first law of geography

机译:制定指示Tobler第一个地理法则的一流公民

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Waldo Tobler frequently reminded us that the law named after him was nothing more than calling for exceptions. This article discusses one of these exceptions. Spatial relations between points are frequently modeled as vectors in which both distance and direction are of equal prominence. However, in Tobler's first law of geography, such a relation is described only from the perspective of distance by relating the decreasing similarity of observations in some attribute space to their increasing distance in geographic space. Although anisotropic versions of many geographic analysis techniques, such as directional semivariograms, anisotropy clustering, and anisotropic point pattern analysis, have been developed over the years, direction remains on the level of an afterthought. We argue that, compared to distance, directional information is still under-explored and anisotropic techniques are substantially less frequently applied in everyday GIS analysis. Commonly, when classical spatial autocorrelation indicators, such as Moran's I, are used to understand a spatial pattern, the weight matrix is only built from distance, without direction being considered. Similarly, GIS operations, such as buffering, do not take direction into account either, with distance in all directions being treated equally. In reality, meanwhile, particularly in urban structures and when processes are driven by the underlying physical geography, direction plays an essential role. In this article we ask whether the development of early GIS, data (sample) sparsity, and Tobler's law lead to a theory-induced blindness for the role of direction. If so, is it possible to envision direction becoming a first-class citizen of equal importance to distance instead of being an afterthought only considered when the deviation from a perfect circle becomes too obvious to be ignored?
机译:Waldo Dobler经常提醒我们,判定他的法律只不过是呼吁例外。本文讨论了其中一个例外。点之间的空间关系经常被建模为距离和方向具有相同突出的载体。然而,在倒置的地理规律中,仅仅通过距离的角度来描述这种关系,通过将一些属性空间中的观测值下降到其增加的地理空间中的距离来描述。虽然多年来已经开发出许多地理分析技术的各向异性版本,例如定向半乐曲造影,各向异性聚类和各向异性点模式分析,但方向仍保持在提前事后的水平。我们认为,与距离相比,仍然探讨了定向信息,并且各向异性技术在日常GIS分析中大大频繁应用。通常,当古典空间自相关指示器(例如Moran的I)被用于理解空间模式时,权重矩阵仅由距离构建,而不考虑方向。类似地,GIS操作,例如缓冲,也不应考虑一下,距离各个方向的距离进行平等。实际上,与此同时,特别是在城市结构中,当流程受到潜在的物理地理的驱动时,方向发挥重要作用。在本文中,我们询问了早期GIS的发展,数据(样本)稀疏和表人的法律是否导致理论引起的方向作用的失明。如果是这样,是否可以设想方向成为一个同等重要到距离的一流公民,而不是在从完美圈子的偏差变得太明显被忽略时被考虑的事后才能被考虑?

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