Calculation of shape similarity between curves is one of the most fundamental and theoretical problems in cartography, graphics, and geometry. Although existing machine learning methods can be used to calculate curve shape similarity, they often rely on extensive sets of sample curves, leading to a low efficiency. To address this issue, this paper proposes a method for directly calculating shape similarity between simple curves. First, two curves are moved, rotated, and scaled to obtain the optimal position where the mean distance between the two curves is the least. Second, the two curves are divided into a number of subsections based on their intersections of the curves. Third, the shape similarity within each subsection (i.e., two sub-curves) is calculated by the principle of proximity in Gestalt. Finally, the shape similarity of the two curves can be obtained by calculating the weighted shape similarity of all subsections. The proposed method is validated through the psychological experiments, and the results show that the calculated shape similarity aligns with human spatial cognition, indicating its practical applicability in specific scenarios. Moreover, the proposed method not only directly calculates curve shape similarity but also eliminates the reliance on a large number of curve samples, resulting in increased computational efficiency. The method presented in this paper provides a more efficient and direct tool for calculating curve shape similarity and holds promise for applications in various fields such as cartography, graphics, and geometry.

Coastal megacities are typically situated in low-lying and densely populated areas. The occurrence of storm surge compound flooding has the potential to result in catastrophic social, economic, and ecological impacts for these coastal cities. The rising sea levels and the increased intensity and frequency of tropical cyclones caused by global warming will exacerbate the challenges faced by coastal cities. Therefore, accurately assessing compound flooding events caused by tropical cyclones is critical to protecting coastal areas from inundation. However, research on the impact of climate change on the risk of tropical cyclone induced compound flooding in coastal areas is still limited. In this study, we used the EC-EARTH3P climate model and selected a dataset of climate change tropical cyclone trajectories synthesized by the STORM model. This dataset is generated using historical data from the International Best Track Archive for Climate Stewardship (IBTrACS) to simulate synthetic tropical cyclones under future climate conditions. Subsequently, we used the coupled Delft3D FLOW & WAVE hydrodynamic model to simulate the impact of storm surge compound water levels on coastal areas due to the nonlinear effects of tropical cyclones wind fields and waves. Furthermore, we investigated the contributions of tropical cyclones and sea level rise to coastal storm surge compound flooding under different Shared Socioeconomic Pathways (SSPs) scenarios, taking the Shanghai city, located within an estuary and along the coastline of China, as our case study. The results showed that climate change had a significant impact on storm surge compound flooding. The future compound flooding disasters exhibited spatial variations in shanghai and differences in water level heights, influenced by future cyclone paths and intensities. Among these areas, Chongming district was the most seriously affected area by storm surge compound flooding. In addition, sea level rise under different climate scenarios will lead to more severe flood hazards in the Shanghai area. We found that although sea level rise will further intensify the impact of storm surge compound flooding in Shanghai, tropical cyclones will have a greater influence on future compound flooding in the city. The spatial risk analysis framework for compound flooding hazards under climate change designed in this study can also be applied to research future storm surge compound flooding hazards in other coastal megacities. Our research findings not only provide a foundational basis for policymakers and flood risk managers to identify risk vulnerable areas, but also provide significant implications for coastal adaptation measures and urban emergency response planning.