基于小波理论的多重分辨率的曲面构造(英文)

Multiresolution Surface Construction

高精度、非接触式的激光数字扫描仪的诞生 ,使得人们能非常方便地获得高细节的物体形状。这种物体是以非结构化和浓密的网格存储在计算机中的。为了在科学、工程、艺术等领域有效地应用这种物体 ,需要建立物体在计算机中有效表达形式。基于小波分析的多重分辨率的曲面构造能担任这种任务。细分连接 (subdivision connection)的小波函数的构造需要我们把曲面参数化到一个简单的复合形域中。在这篇文章中 ,我们从微分几何的测地极映射观点出发 ,提出用快速的形状保持的参数化方法有效地建立具有多重分辨率的物体曲面形状。同前面的方法相比 ,我们的构造过程可以节约大量的计算时间且维持良好的物体曲面形状。

Unstructured and highly detailed meshes need to be effectively represented in many applications. Accompanied with wavelets, hierarchical multiresolution meshes can be in charge of this effective representation. To perform this multiresolution representation with wavelets, an available function space needs to be constructed and defined over the general triangulated surface meshes. To employ an effective method to accomplish the construction of a continuous parameterization of arbitrary meshes over a simple domain is a key problem. The paper proposes a fast parameterization method based on geodesic polar map that can be effectively served in multiresolution surface construction. Compared with previous methods, the construction process given in the paper can save a lot of computation time and maintain fine visual result.