中文摘要：

我们在场统一的一个多水平分区为能被设计或在一种含蓄的形式代表的表面重建的代数学的集合表面(MPU-APSS ) 。代数学的点集合表面(APSS ) 用本地移动从一套未组织起来的点定义光滑的表面最少平方(MLS ) 代数学的范围适合。由于本地性质，然而， APSS 不为几何学编辑并且当模特儿工作很好。相反，我们的方法基于统一途径的分区为散布的点集合造一个含蓄的近似函数。由使用 octree 分策略，我们适应地首先为点集合构造本地代数学的范围，然后使用 weighting 功能一起混合这些本地形状功能。最后，我们从表面计算签署的距离功能的控制错误的近似。另外，我们在场为点使我们的表示合适的一个有效设计操作员设定过滤并且动态点采样。我们为表面重建并且几何学当模特儿例如表面结束表明我们的统一途径的有效性。

英文摘要：

We present a multi-level partition of unity algebraic set surfaces （MPU-APSS） for surface reconstruction which can be represented by either a projection or in an implicit form. An algebraic point set surface （APSS） defines a smooth surface from a set of unorganized points using local moving least-squares （MLS） fitting of algebraic spheres. However, due to the local nature, APSS does not work well for geometry editing and modeling. Instead, our method builds an implicit approximation function for the scattered point set based on the partition of unity approach. By using an octree subdivision strategy, we first adaptively construct local algebraic spheres for the point set, and then apply weighting functions to blend together these local shape functions. Finally, we compute an error-controlled approximation of the signed distance function from the surface. In addition, we present an efficient projection operator which makes our representation suitable for point set filtering and dynamic point resampling. We demonstrate the effectiveness of our unified approach for both surface reconstruction and geometry modeling such as surface completion.