Adaptive meshing of non-manifold parametric patch complexes with shared-curve compatibilityImage 999

We present an adaptive meshing technique for non-manifold parametric patch complexes with explicit shared curves. The method assumes that these shared curves are explicit entities of the input topology and preserves their discretization during refinement. Starting from a coarse patch-consistent mesh, each iteration evaluates curvature mismatch, updates patch- and curve-level refinement factors, rediscretizes shared curves, and rebuilds triangular patch interiors in the parametric domain using a hybrid quadtree-guided and advancing-front strategy. Shared-curve samples are stored once and reused by all incident patches, including curves incident to three or more patches, which preserves boundary compatibility by construction. Beyond this invariant, the technique integrates factor-driven curvature adaptation, conservative curve-level refinement, quadtree-supported interior sizing, and feature-aware advancing-front reconstruction to obtain compatible triangular patch meshes. The method is evaluated using normalized global error, triangle-shape quality, and a compatibility metric used to verify the shared-curve invariant and to compare against unsynchronized baselines. Across three evaluation cases, the approach reduces normalized global error by 74% to 96% while maintaining zero mean compatibility error. Controlled internal comparisons indicate that shared-curve synchronization is the mechanism responsible for boundary coherence, whereas hybrid reconstruction provides the strongest geometric improvement. The results support compatibility-preserving adaptive rebuilding as a practical strategy for controlled planar, curved, and mixed non-manifold patch configurations that satisfy explicit patch–curve assumptions.