# A Blockchain Copyright Protection Model Based on Vector Map Unique Identification
## 3 Basic Idea and Preliminaries
### Vector Map Unique Identification Based on Geometric and Topological Relationships  
As the ID number of a map, unique identification is obtained by computing the unique characteristic values of a vector map. The purpose of this is to replace the cumbersome map files registered on the blockchain platform while ensuring uniqueness and robustness, thereby replacing the traditional deployment method of map files on the blockchain platform. The construction approach of unique identification in this paper is as follows: utilizing geometric relationships [38], such as angles between geographical features, a quantitative description of the map structure is obtained through mathematical calculations and geometric measurements. Simultaneously, based on the topological feature relationships [39] of the vector map dataset, an analysis of proximity, connectivity, and containment relationships between geographic entity features is conducted to abstract the mathematical expressions of topological relationships [40]. Ultimately, by combining geometric and topological features, unique feature identification is performed for the map, ensuring not only the uniqueness of the identification but also resistance to changes in geographic features and geometric attributes. Firstly, all coordinate points of the vector map dataset are obtained, after which a Delaunay triangulation \(T\) is constructed. Subsequently, all circles inscribed in triangles adjacent to each coordinate point \(P_{i}\) are identified. The minimum radius of these inscribed circles corresponds to the angle \(\theta\), as illustrated in Figure 3.  
Figure 3: Schematic diagram of angle feature parameter acquisition. Working according to the aforementioned approach, it is necessary to obtain the angular value \(\theta\) for each geographical feature, forming the geometric feature vectors of the vector map. \[AN_{i}=[\theta_{1},\theta_{2},\ldots,\theta_{length}] \tag{1}\]  
where _length_ denotes the number of geographical features in the vector map dataset. As depicted in Equation (2), by mapping the angle values, a quantitative expression of geometric features is achieved, thereby obtaining the geometric feature parameter \(H_{ijk}\). \[H_{ijk}=floor[(AN_{i})^{\frac{1}{2}}\times(n-1)]+1 \tag{2}\]  
where \(p\) serves as an adjustable parameter that modulates the weighting effect, with smaller values of \(p\) amplifying the weighting effect, while larger values diminish it. \(n\) denotes the length of subsequent unique identification sequences. The floor(\(x\)) function is utilized to obtain the largest integer less than or equal to \(x\). Subsequently, each geographical feature in the vector map dataset is traversed. It is necessary to consider the entire vector dataset \(S\), which includes a set of points \(P\), a set of polylines \(L\), and a set of polygons \(A\). Using the R-tree index \(R\), it is necessary to perform nearest non-intersecting heterogeneous feature queries for each feature \(i\), leveraging spatial indexing to accelerate distance computations. The algorithm for nearest neighbor non-intersecting heterogeneous feature queries across diverse feature types is outlined as follows:  
\[NN(i)=\arg_{j\in S,j\
eq i,type(i)\
eq type(j)}d(i,j) \tag{3}\]  
where type(\(i\)) denotes the type of feature \(i\). The distance \(d(i,j)\) is measured by using the Hausdorff distance as the metric for different types of features. Assuming that feature \(i\) and feature \(j\) belong to different subsets of \(S\) (i.e., \(i\in P\) and \(j\in L\) or \(A\), or \(i\in L\) and \(j\in P\) or \(A\), or \(i\in A\) and \(j\in P\) or \(L\)), the distance computation formula is as follows:  
\[d(i,j)=\max\left\{\underset{x\in i}{\text{supinf}}\|x-y\|,\underset{y\in j}{ \text{supinf}}\|x-y\|\right\} \tag{4}\]  
where \(\|\cdot\|\) denotes the Euclidean distance.