Topology
The so-called "topology" is a method of abstracting entities into "points" that have nothing to do with their size and shape, and abstracting the lines connecting entities into "lines", and then expressing the relationship between these points and lines in the form of graphs. Its purpose It is to study the connection between these points and lines. A graph showing the relationship between points and lines is called a topology graph. Topological structure and geometric structure belong to two different mathematical concepts. In geometric structure,
what we want to investigate is the positional relationship between points and lines, or geometric structure emphasizes the shape and size of points and lines. For example, trapezoids, squares, parallelograms and circles all belong to different geometric structures, but from the perspective of topological structure, because the connection relationship between points and lines is the same, they have the same topological structure, that is, ring structure. In other words, different geometric structures may have the same topological structure.
Topological space
Topology—The word comes from Greek, and its original meaning is "the study of shapes." Topological properties refer to geometric properties that can remain unchanged under topological transformation (arbitrary expansion or deformation, but no kinking or folding). Several important topological characteristics that the research of geospatial relations pay special attention to are connectivity, inclusion, and adjacency. 1. Connectivity. The intersection of the space curves is often called a node. Connectivity...
Topology—The word comes from Greek, and its original meaning is "the study of shapes." Topological properties refer to geometric properties that can remain unchanged under topological transformation (arbitrary expansion or deformation, but no kinking or folding). Several important topological characteristics that the research of geospatial relations pay special attention to are connectivity, inclusion, and adjacency.
1. Connectivity. The intersection of the space curves is often called a node. Connectivity refers to the interconnection of curves or arcs at nodes. In the following figure, the figure in figure a is greatly deformed as shown in figure b, but the connection relationship of curves or arcs does not change, for example, arcs 1, 2, 3 are still connected at node 4; arcs Segments 2, 5, and 6 are still connected at node B. It can be seen that "connectivity" is a topological characteristic.
2. Include. Inclusion relations are sometimes only in terms of polygons or regions, but we adopt a broader understanding here to include all inclusion relations or composition relations that can be defined between points, lines, and surfaces into the category of inclusion. For example, a point is on a line or its end points are on or inside the boundary of an area or polygon; a line is inside a polygon; an area is inside another area, etc. Comparing the figures a and b in the above figure, it can be confirmed that these spatial relationships remain unchanged in the topological transformation.
A small area located inside a larger area is often called an "island". For example, in the figure below, the small area enclosed by curve 4 is an "island" in the large area enclosed by curves 2, 3, and 6.
There are two basic composition relationships in G1S worth noting. First, a line can be made up of a series of points. As mentioned above, the curve in the geographic information system is actually composed of many sufficiently small line segments. Therefore, as long as the computer provides the coordinate series of the nodes of all the line segments of a curve, the curve can be determined. Second, a region or a polygon is surrounded by several lines, which is also called "polygonal region definition". For example, in the above figure, curves 2, 3, 4, and 6 enclose a ring-shaped area, which defines polygon I. In the topological transformation, although the shape changes, the characteristic that this ring-shaped area is surrounded by curves 2, 3, 4, and 6 is also unchanged.
Adjacency. Contiguity refers to the adjacency relationship between two regions that share a common edge. As shown in the figure above, polygons I and n with curve 6 as the common edge are adjacent regions. This kind of adjacency will not change due to topology transformation.
If the direction is specified for the common edge, the adjacency can be further described as "right neighbor" or "left neighbor". For example, in the above figure, suppose we specify curve 6 to take the direction shown in the figure, then, looking in this direction, polygon I is the left neighbor, or left polygon, and polygon II is the right neighbor, or right polygon. If the trend of curve 6 is reversed, then the relationship between the left neighbor and the right neighbor will also be reversed.
Topological functions in GIS
1. ST_3DIntersects #Intersect
2. ST_Contains #include
3. ST_ContainsProperly #Fully included
4. ST_Covers #cover
5. ST_CoveredBy #is covered
6. ST_Crosses #Space Intersection