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Cartesian meshes based on the immersed boundary method are widely adopted for their convenience in implementing automated mesh generation. The performance of Cartesian mesh generation, particularly for complex geometries, is a crucial factor that directly impacts the efficiency of computational fluid dynamics solutions. In this study, we present an innovative strategy for efficient Cartesian mesh generation. Our methodology centers around the inner product test (IPT), enabling precise and efficient interior/exterior determination for intersected Cartesian cells. For this purpose, we enhance the k-d tree based intersection determination process to provide essential information of surface mesh for IPT, while concurrently improving the efficiency of the determination process. Our new methods offer automatic generation capabilities for arbitrary complex geometries. Through a series of tests, the new methods illustrate the notable performance improvements with the generation time of less than 4 min for the Cartesian mesh with 108 cells. Overall, our work optimizes Cartesian mesh generation for complex geometries, presenting significant potential for addressing the challenges of moving boundary problems. [ABSTRACT FROM AUTHOR]