Open surface components prevail in real industrial 3D content and support rendering, physical simulation and geometric editing. Garments serve as a typical open surface type, with numerous existing generation methods leveraging sewing patterns to generate 2D panels and stitch them into 3D shapes. Such domain-specific designs lack scalability and cannot generalize to shoes and accessories. Common field-based 3D generators prioritize watertight meshes and tend to create flawed double-layer structures on open surfaces. Though Trellis2 adopts field-free representation, its open surface results still contain normal and topology errors. We present AnySurf, a unified framework generating open, closed and hybrid 3D surfaces with accurate face orientation. Built on directed-edge enhanced Flexible Dual Grid (FDG-D), our representation retains normal direction information via oriented grid edges. We also propose ROS-FT post-training and a lightweight DE-Adapter with merely 1% extra parameters, facilitating directed edge learning while preserving original generation performance. We further construct Outfit3D dataset containing industrial garments and closed accessories. Our work transforms garment modeling into a universal 3D generation task. Experimental results demonstrate superior mesh quality and better practicality for downstream applications.