## 1 Introduction
selected structural parameters, metric parameters, and statistical parameters to construct a polygon complexity model [25]. [PERSON] et al. used the absolute curvature to quantify the surface shape complexity of objects [26]. [PERSON] et al. used the number of polygon features and the number of vertices of each feature to quantify the complexity of objects and, based on this, achieved reasonable data partitioning in parallel computing [27]. [PERSON] et al. defined a complexity calculation method for line elements and area elements based on two indicators, namely, an area coefficient and an angle coefficient, and quantified the geometric information of sensitive elements in digital maps [28]. However, although this method partially solves the problem of measurement complexity in geographic calculations, it does not reflect the relationship between shape complexity and the computational efficiency of an overlay analysis algorithm. [PERSON] et al. selected 27 shape variables and used a stepwise multiple linear regression method to establish a shape complexity model [29], which effectively explained the relationship between complexity and algorithm efficiency; however, this shape complexity model was not applied to vector data partitioning. With the continuous development of the field of spatial overlay analysis, many polygon clipping algorithms with different characteristics have emerged. Common polygon clipping algorithms include the Wang algorithm [30], the Liang-Barsky algorithm [31], the Sutherland-Hodgeman algorithm [32], the Weiler-Atherton algorithm [33], the Vatti algorithm [34], the Greiner-Hormann algorithm [35], the [PERSON] algorithm [36], and the Mar [PERSON] algorithm [37]. All of these algorithms have their own advantages and disadvantages. The Wang algorithm and the Liang-Barsky algorithm apply only to arc polygons. The Sutherland-Hodgman algorithm can be used to clip only arbitrary polygons and convex polygons. The Weiler-Atherton algorithm can be used to perform the overlay analysis of concave polygons and convex polygons, but there is a possibility of failure when dealing with the superposition of overlapping edges. Compared with the Greiner-Hormann algorithm, [PERSON]'s algorithm offers no substantial improvement, and the algorithm proposed by [PERSON] et al. has not been widely used [19]. The Greiner-Hormann algorithm and the Vatti algorithm are generally recognized as effective algorithms that can address arbitrary polygon clipping problems in a limited time and obtain correct results. However, according to the experimental results of [PERSON] et al., the computational efficiency of the Greiner-Hormann algorithm may be lower than that of the [PERSON] algorithm [37]. Therefore, the Vatti algorithm is selected as the clipping algorithm in this paper. In summary, previous scholars have carried out a lot of research on vector data partitioning and polygon shape complexity measurement and have achieved certain results, but there are some shortcomings. The current data partitioning method cannot fully consider factors such as polygon spatial characteristics and shape characteristics, resulting in unbalanced data after grouping; the measurement of shape complexity cannot fully reflect the relationship with the performance of the overlay analysis algorithm. In view of the above considerations, this paper combines shape complexity measurement with data partitioning to establish a shape complexity model that can effectively explain algorithm performance and applies it to the partitioning of vector data to make the grouped data complexity similar and achieve data balance. Using two kinds of vector data with different amounts of data, the intersection operator and difference operator of the Vatti algorithm are taken as examples for multicore parallel comparative analysis.