Abstract: Many emerging applications, from computational biology to digital twins and urban planning, rely heavily on three-dimensional spatial joins over polyhedral meshes. These joins comprise computationally-intensive triangle--triangle intersection tests that pairwise compare the faces of polyhedral meshes. Since each mesh may contain thousands of faces, the resulting cost challenges the responsiveness of spatial data management techniques. Existing techniques follow the filter-and-refine paradigm, accelerating either the filtering step through indexing or the refinement step through progressive mesh compression combined with GPU parallelization of triangle--triangle tests. However, the former neglects the high cost of intra-geometry refinements, whereas the latter lowers this cost but still relies on the same pairwise triangle--triangle tests. In this paper, we introduce Pierce, an approach that reformulates three-dimensional spatial joins over complex polyhedral meshes as ray-tracing operations and leverages the hardware ray-tracing units (RT cores) of modern GPUs to accelerate query execution. Our approach casts rays along the edges of one mesh against a spatial hierarchy built over the other, performing ray--node tests at the internal levels to prune distant geometries and ray--triangle tests at the leaves to identify intersecting meshes, both of which RT cores accelerate in hardware. We evaluated Pierce on real and synthetic data against multiple baselines, demonstrating more than two orders of magnitude speedup on digital pathology data compared to the state-of-the-art approach.