With the continuous expansion and complexity of exploration engineering, traditional geological exploration methods are no longer able to meet the needs of real-time monitoring and accurate analysis. The Delaunay triangulation algorithm, as a spatial data analysis tool, can help engineers and geologists better understand underground structures, geological changes, and potential safety risks, and is expected to bring revolutionary changes to the field of geological exploration engineering. This article uses the analysis of geological data visualization, groundwater flow simulation, and seismic wave propagation simulation to draw the following conclusion through two sets of simulation experiments: the application of Delaunay algorithm in quality and safety monitoring of geological exploration drilling engineering improves the accuracy of drill bit temperature prediction by about 5% compared to traditional schemes, and at the same time, the stability of geological stress is improved by about 11.2%. This study can optimize the triangulation of geological exploration point cloud data, improve the spatial representation accuracy of underground structures, and provide a more reliable foundation for the design and implementation of exploration and drilling engineering.