Type-Free Global Intersection Analysis with Linear Displacement Fields

History-independent intersection repair is a critical bottleneck in physical simulation and geometric processing. Existing global intersection analysis (GIA) methods identify invalid regions of relatively small area, but they rely on type-specific heuristics for different contour categories, while local intersection contour minimization (ICM) methods are simpler to deploy but often stall in local minima under deep or nested penetrations. In this paper, we present a novel untangling framework that formulates intersection resolution as a minimum-displacement separation-direction problem. For each intersection contour, we test a set of candidate linear displacement directions using VF/EE/FV ray casting and filter the raw hits using cluster culling based on primitive adjacency to find the valid hits belonging to the penetration region. We rank candidate directions by displacement cost, and refine the most promising direction with projected Newton updates on the sphere. Finally, we convert the valid hit support into standard proximity-style penalty pairs and integrate them into the standard physics simulator. We evaluate our method on diverse contour configurations and self-intersection benchmarks. Compared with the GIA and ICM baselines, our method resolves intersections more consistently, particularly in challenging cases involving deep and nested layers. The results show that our method is a practical, solver-compatible untangling pipeline for complex mesh intersections.