Thin surfaces, such as the leaves of a plant, pose a significant challenge for implicit surface reconstruction techniques, which typically assume a closed, orientable surface. We show that by approximately interpolating a point cloud of the surface (augmented with off-surface points) and restricting the evaluation of the interpolant to a tight domain around the point cloud, we need only require an orientable surface for the reconstruction. We use polyharmonic smoothing splines to fit approximate interpolants to noisy data, and a partition of unity method with an octree-like strategy for choosing subdomains. This method enables us to interpolate an $N$-point dataset in $\mathcal{O}\left(N\right)$ operations. We present results for point clouds of capsicum and tomato plants, scanned with a handheld device. An important outcome of the work is that sufficiently smooth leaf surfaces are generated that are amenable for droplet spreading simulations.

薄表面（例如植物的叶子）对隐式表面重建技术提出了重大挑战，这些技术通常假定为封闭的、可定向的表面。我们表明，通过对表面的点云进行近似插值（用表面外点增强）并将插值的评估限制在点云周围的紧密域中，我们只需要一个可定向的表面来进行重建。我们使用多谐平滑样条来拟合噪声数据的近似插值，以及使用类似八叉树的策略来选择子域的统一方法的分区。这种方法使我们能够插入一个$N$- 点数据集在 $\mathcal{哦}\left(N\right)$操作。我们展示了用手持设备扫描的辣椒和番茄植物点云的结果。这项工作的一个重要成果是生成了足够光滑的叶片表面，可用于液滴扩散模拟。