With advancements in geometric deep learning techniques, neural signed distance functions (SDFs) have gained popularity for their flexibility. Recent studies show that neural SDFs can retain geometric details and encode sharp features. However, during the mesh extraction stage, methods like marching cubes may degrade these geometric details and sharp features, thus compromising the expressiveness of neural SDFs. In this paper, we aim to develop a general-purpose mesh extraction method for both freeform and CAD models, assuming the availability of a SDF. Our goal is to produce a well-triangulated, resolution-adjustable mesh surface that preserves rich geometric details and distinct feature lines. Our approach is inspired by Centroidal Voronoi Tessellation (CVT) but introduces two key modifications. First, we extend CVT computation to implicit representations, where explicit surface decomposition is not available. Second, we propose a measure for estimating the likelihood that a point lies on feature lines, enabling the extraction of feature-aligned triangle meshes using power diagrams (with site weights positively correlated to the likelihood values). Comprehensive comparisons with state-of-the-art methods demonstrate the superiority of our approach in both feature alignment and triangulation quality.