Global Discrete Optimization for Quad-Dominant Mesh Reduction

We present a global, discrete optimization framework for quad-dominant mesh reduction that formulates simplification as an edge selection problem under coupled topological and geometric constraints. Unlike greedy edge-collapse heuristics, which make irreversible local decisions, and rigid poly-chord removal schemes, which over-constrain global structure, our method casts quad-dominant reduction as an Integer Linear Programming (ILP) problem that jointly optimizes edge flow continuity and geometric fidelity in a single global optimization. To make this formulation both tractable and adaptive, we segment poly-chords at geometrically meaningful breakpoints to relax otherwise rigid topological constraints, and introduce geometry-aware soft constraints that steer the optimization toward preserving high-curvature and deformation-critical regions. Extensive experiments demonstrate that our approach consistently outperforms state-of-the-art methods in preserving quad structure and edge flow, while achieving competitive geometric accuracy and significantly benefiting downstream editing applications.