提出一种无需网络的光滑曲面表示,可无缝融合局部贴图。
Blended Chart Surfaces: A Seamless Explicit Representation for Smooth Surface Fitting

- 用代理网格和多项式映射构建局部贴图,通过平滑融合实现全局光滑。
- 表面全局光滑且可微,直接支持法向量与曲面能量等微分量计算。
- 适合需要精确微分信息的几何优化任务,如逆设计或物理模拟。
适用于几何处理的曲面表示应具备紧凑性、显式性、全局光滑性、广泛拓扑支持及可靠的微分量访问能力,同时兼容现代可微优化。现有神经表示通常牺牲其中一项:隐式场需等值面提取,显式神经映射受限于标准域参数化或存在局部贴图间接缝。本文提出Blended Chart Surfaces,一种无网络、紧凑、显式的曲面表示,其光滑性由构造保证,并锚定于用户提供的拓扑。给定编码目标拓扑与近似几何的粗略代理网格,该方法在每个代理顶点上联合优化多项式映射,使用现成优化器拟合隐式目标形状,避免输入参数化需求。邻近映射通过平滑的'一环坐标'融合方案合并,解耦拓扑与粗略几何(由代理携带)与几何细节(由局部块携带)。表面全局光滑、完全可微,可稳定计算导数,使微分量与曲面能量直接可用。此外,该构造对代理网格的刚体变换和缩放具有等变性。我们在多种拓扑与几何复杂度下评估该方法,并与插值函数基线及网格位移MLP等显式方法对比。结果表明,Blended Chart Surfaces在紧凑性、简洁性、微分量访问与表达力之间取得良好平衡,且跨贴图边界保持光滑。
原文摘要 · Abstract (English)
A surface representation suitable for geometry processing should be compact and explicit, provide global smoothness guarantees, support a wide range of surface topologies, and offer reliable access to differential quantities such as normals and surface energies, while remaining compatible with modern differentiable optimization. Existing neural representations typically sacrifice one or more of these properties: implicit fields typically require iso-surfacing for downstream use, while explicit neural maps are constrained by canonical-domain parametrizations or exhibit seam artifacts between local charts. We introduce Blended Chart Surfaces, a compact, network-free, explicit representation that is smooth by construction and anchored to user-provided topology. Given a coarse proxy mesh encoding the intended surface topology and approximate geometry, Blended Chart Surfaces jointly optimize for a polynomial map at each proxy vertex using an off-the-shelf optimizer to fit to an implicit target shape, avoiding the need for an input parametrization. Neighboring maps are fused using a smooth 'one-ring coordinate' blending scheme, decoupling topology and coarse geometry (carried by the proxy) from geometric details (carried by the local patches). The surface is globally smooth, fully differentiable, and enables stable evaluation of derivatives, making differential quantities and surface energies directly accessible. Additionally, our construction is equivariant to rigid motions and scaling of the proxy mesh. We evaluate Blended Chart Surfaces on various topologies and geometric complexity, and compare against explicit alternatives including interpolating-function baselines and mesh-displacement MLPs. Across these, Blended Chart Surfaces achieve a favorable trade-off among compactness, simplicity, access to differential quantities, and expressivity while remaining smooth across patch boundaries.
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