Feature-Preserving Cage Construction based on Signed Distance Field

We propose a novel automatic approach to construct low-complexity, manifold, and non-self-intersecting cages, which preserves geometric features, maintains tight enclosure, enforces symmetry, and produces high-quality meshes. The method is realized through a coherent three-stage pipeline. Starting with isosurface extraction from the Signed Distance Field (SDF), our method inherently enforces envelope and non-self-intersection properties via density field modification and leverages sharp features of the input to drive a shape-preserving initial cage. Second, a constrained Quadric Error Metric (QEM) simplification problem is solved using a geometry-driven push-pull strategy, decimating the initial cage to a user-specified vertex count. This yields a concise intermediate structure while preserving the fundamental properties. Finally, we introduce a symmetry-aware refinement stage via an integrated optimization that simultaneously preserves symmetry, improves mesh quality, and ensures tight alignment with the input. We evaluate symmetry using a deviation metric (SDE) to extract a symmetry plane and produce a symmetry-consistent cage, followed by mesh quality enhancement and collision-free enforcement. Through extensive experiments on diverse models, including evaluations on public benchmarks, we demonstrate that our method outperforms existing techniques in handling complex shapes, automatically preserving features and symmetry while generating a compact, coarse cage.