An advancing-ridge approach for recovering boundary $(d-1)$-simplices in $d$-dimensional meshes
This study addresses the challenge of high-dimensional boundary-constrained mesh recovery in four-dimensional spacetime simulations by proposing an advancing front algorithm based on (d−2)-simplex ridges. The method innovatively integrates a constrained cavity operator with an incremental Steiner point insertion strategy to effectively ensure geometric consistency and topological correctness of complex boundaries. Experimental results demonstrate that the algorithm achieves a boundary recovery rate exceeding 99% in four-dimensional scenarios, generating 300 million pentatopes within merely 15 minutes. These findings indicate a significant breakthrough in overcoming efficiency and robustness bottlenecks associated with high-dimensional constrained mesh generation, thereby providing reliable computational support for large-scale spacetime numerical simulations.