# Space transformation

Geographic information systems usually establish spatial databases based on meaningful layers and corresponding attributes. In order to meet the needs of specific spatial analysis, a series of logical or algebraic operations on the original layer and its attributes are needed to generate new geographical layers with special meanings and their attributes, this process is called spatial transformation. Spatial transformations can be based on a single layer, or on multiple layers, this chapter limits spatial transformation to operations or calculations on a single layer, multi-layer operations are described in overlay analysis.

Spatial data in GIS can be divided into vector and raster data structures. Due to the vector structure contains a lot of topological information and the data organization is complex, the spatial transformation is very complicated. The grid structure is simple and regular, and the spatial transformation is easy. In addition, the space transformation based on vector structure is of little significance to a single layer, when generating a new layer, the information of multiple layers is often needed, which is of great significance in multi-layer overlay analysis.

Spatial transformation based on grid structure can be divided into three ways: (1) single point transformation; (2) neighborhood transformation; (3) region transformation.

Single-point transformation only considers the attribute value of a single point, and assumes that the transformation of an independent unit does not depend on the attributes of its neighbors, nor is it affected by the general characteristics of the region. The most common functions of single point transformation are algebraic operations such as addition, subtraction, multiplication and division, logical operations such as sum, union, non-exclusion or exclusion, comparative operations such as greater or less, exponential functions, logarithmic functions, trigonometric functions, etc. The new layer can be completely different from the original layer.

The neighborhood transform means that when calculating the value of a new layer primitive, not only the value of the corresponding primitive itself on the original layer, but also the influence of other primitive values associated with the primitive. This association can be a direct geometric association or an indirect geometric association. Common functions include smooth, discrete point search, continuous surface description (slope, aspect, visual field analysis), point judgment in polygons, etc.

The area transformation means that when calculating the value of a new layer attribute, the attribute value of the entire area is considered, that is, a function is used to synthesize all the values in a certain area, and then the new attribute value is calculated. Common functions include methods such as region mean, mode, extremum, summation, grouping, and overall interpolation.