基于三角形的空间和时空数据仿射不变查询逻辑
A triangle-based logic for affine-invariant querying of spatial and spatio-temporal data
摘要：
在空间数据库中，由于原点或测量单位的不同选择（例如，厘米对英寸）。通过以仿射不变的方式表示和查询数据，我们可以避免这些不兼容性。在实践中，空间（分别为，时空）数据通常被表示为三角形的有限并集（分别，移动三角形）。由于两个任意三角形在平面的唯一亲和度上相等，因此它们似乎是作为仿射不变查询语言的基本单元的完美候选者。我们提出了一个所谓的“三角逻辑”，一个查询语言，是仿射通用的，三角形作为基本元素。我们表明，这种语言具有相同的表达能力的仿射通用片段的一阶逻辑在三角形数据库上的实数。我们说明，所提出的语言是简单和直观的。它也可以作为迈向时空数据的“移动三角逻辑”的第一步。
英文摘要：
In spatial databases, incompatibilities often arise due to different choices of origin or unit of measurement (e.g., centimeters versus inches). By representing and querying the data in an affine-invariant manner, we can avoid these incompatibilities. In practice, spatial (resp., spatio-temporal) data is often represented as a finite union of triangles (resp., moving triangles). As two arbitrary triangles are equal up to a unique affinity of the plane, they seem perfect candidates as basic units for an affine-invariant query language. We propose a so-called "triangle logic", a query language that is affine-generic and has triangles as basic elements. We show that this language has the same expressive power as the affine-generic fragment of first-order logic over the reals on triangle databases. We illustrate that the proposed language is simple and intuitive. It can also serve as a first step towards a "moving-triangle logic" for spatio-temporal data.
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