Tyson polygons, Tyson polygons and their applications.

Tyson polygons and their properties.

The Dutch climatologist A. H. Thiessen proposed a method of calculating the average rainfall based on the rainfall of discretely distributed weather stations, that is, all adjacent weather stations were connected into triangles and made a vertical bisector on each side of these triangles, so that a number of vertical bisectors around each weather station were enclosed into a polygon. The intensity of rainfall in the area of this polygon is expressed by the intensity of rainfall at a unique weather station contained within this polygon, and this polygon is called a Tyson polygon. As shown in Figure 5-6-1, the polygon formed by the dotted line is the Tyson polygon.

Each vertex of a Thiessen polygon is the center of the circumscribed circle of each triangle. Thiessen polygons are also known as voronoi diagrams, or dirichlet diagrams.

Figure 5-6-1 Tyson polygon.

The characteristics of Tyson polygons are:

1. Each Tyson polygon contains only one discrete point data;

2. The distance between the point in the Tyson polygon and the corresponding discrete point is the closest;

3. The distance from the point on the edge of the Thiessen polygon to the discrete points on both sides of it is equal.

Thiessen polygons can be used for qualitative analysis, statistical analysis, proximity analysis, and more. For example, the properties of the Tyson polygon region can be described in terms of the properties of discrete points; The data of discrete points can be used to calculate the data of the Thiessen polygon region; When judging which discrete points are adjacent to other discrete points, it can be directly obtained according to the Thiessen polygon, and if the Thiessen polygon is n-sided, it is adjacent to n discrete points; When a data point falls into a Thiessen polygon, it is closest to the corresponding discrete point, and the distance is not calculated.

In the construction of Thiessen polygons, discrete points are first triangulated. This type of triangulation is called delaunay triangulation.

Come and give it away, I don't mind.

Not sure what questions you ask.

Tyson polygon parity and its application.

Correct answer: Tyson polygon generates the boundary of the polygon from a batch of discrete sampling point data with a certain distribution, and determines the region with the most obvious influence of several discrete sampling points, and the attributes of this region can be represented by the attribute data of sampling points. Tyson polygons have the following properties:

Each Thiessen polygon contains only one discrete data point; The distance between any point within a Tyson polygon and the discrete data points contained in the polygon is less than the distance between it and any other discrete data points; Any vertex of a Tyson polygon must have three edges connected to it, which are the common edges of two or two splices of three adjacent Tyson polygons; If there are three discrete data points around any vertex in a Tyson polygon, and when they are joined into a triangle, the center of the circumscribed circle of the triangle is the vertex. In the field of geoscience, it is often necessary to deal with large amounts of discrete data that are geographically dispersed. Thiessen polygon can automatically generate an isovalue region centered on the sampling point according to the location distribution of the sampling point, so that the attribute data of the sampling point can be expanded into the area attribute data of the region, which has important practical value in the field of geoscience.

In practice, it is not possible to obtain surface attribute data directly due to the constraints of many geoscientific characteristics, and representative sampling point data are often used for estimation. For example, in order to understand the groundwater level, it is necessary to select several sites to drill wells and measure them, and finally estimate the distribution of groundwater level in the area from the data of the measurement points. The choice of discrete data points is important when solving these kinds of problems.

In general, the following points should be taken into account when choosing discrete data points: There are a fair number of discrete data points. Since the number of polygons is equal to the number of points used in discrete data, if the number of sampling points is too small, the described regional properties will be too rough and have no practical significance. The discrete data points selected should be typical, typical, and representative.

What are the characteristics of Tyson polygons? How to set it up?

Correct answer: Tyson polygons can be used for qualitative analysis, statistical analysis, proximity analysis, etc., and their characteristics are: each Tyson polygon contains only one discrete point data; The point within the Tyson polygon is closest to the corresponding discrete point; Points on the edge of a Thiessen polygon are at equal distances from discrete points on either side of it.

Steps to establish Tyson polygons: The key to establishing Tyson's polygon roaming algorithm is to reasonably connect discrete data points into a triangulation network, that is, to construct a delaunay triangulation network. The Zhiqing steps to build a Tyson polygon are:

1) Discrete points automatically build a triangulation, that is, build a delaunay triangulation. For the number of discrete points and the triangles formed, record which three discrete points make up each triangle. 2) Find the numbers of all the triangles adjacent to each discrete point and record them.

This is to find all the triangles with the same vertex in the built triangulation. 3) Sort the triangles adjacent to each discrete point in a clockwise or counterclockwise direction so that the next step joins to generate a Thiessen polygon. 4) Calculate the circumscribed circle center of each triangle and record it.

5) According to the adjacent triangles of each discrete point, connect the center of the circumscribed circle of these adjacent triangles, that is, obtain a Thiessen polygon. For the Tyson polygon at the edge of the triangulation, a vertical bisector can be used to intersect the profile, and together with the profile, the Tyson polygon can be formed.

The steps are as follows: the discrete points automatically construct a triangulation, that is, to construct a delaunay triangulation network, number the discrete points and the triangles formed, and record the three discrete points formed by each triangle; Record the numbers of all triangles adjacent to each discrete point; The triangles adjacent to each discrete point are sorted in a clockwise or counterclockwise direction so that they can be connected to form a Tyson polygon, let the discrete point be O, set a triangle with hole O as the vertex as A, set the other vertex of triangle A except O as A, and the other vertex as F, the next triangle must take of as the side to form the triangle F, the other vertex of the triangle F is E, and the next triangle is infiltrated with OE as the edge, and repeat until it coincides with the Oa edge; Calculate and record the circumscribed circle center of each triangle; According to the adjacent triangles of each discrete point, the center of the circumscribed circle connecting the adjacent triangles can obtain a Tyson polygon, and the Tyson polygon at the edge of the triangular network can be intersected with the contour by a perpendicular bisector line, and the contour forms a Tyson polygon.

1.Determine the color and style of the Tyson polygon: This is a step in materializing the Tyson polygon after it has been drawn, not a necessary step in drawing the Tyson polygon.

2.Choose the tool to draw the Thiessen polygons: This is done in specific drawing software, not the steps to draw the Thiessen polygons.

3.The order in which the Thiessen polygons are drawn: Since the Thiessen polygons are connected by the outer centers of the circles, the order in which they are drawn does not affect their shape and structure, and is therefore not a necessary step in drawing the Thiessen polygons.

The Tyson polygon, also known as the Voronoi Diagram (Voronoi Diagram), is named after Georgy Voronoi, which is a set of continuous polygons composed of vertical plain letter lines connecting two adjacent point segments. The distance from any point within a Tyson polygon to the control points that make up that polygon is less than the distance from the other polygon control points. Innovative thinking using fractals.