摘要
可展曲面是每点高斯曲率均为0的曲面,具有许多良好的性质,因此在工业中具有很多应用.将一般的曲面用可展曲面来逼近表示具有现实意义.以此为目的,文中设计了一个有效的算法来处理一般的曲面,使得处理后的曲面尽可能满足可展的性质,同时与初始的曲面尽量地接近.首先利用最小范数方法来对网格曲面进行处理,得到初始预测的网格曲面.初始预测曲面具有良好的可展性,但是不能较好地保持网格的局部结构.然后利用尽可能刚性(As-rigid-as-possible)的方法,在初始预测曲面的基础上进行修正得到新的网格曲面.为了保持局部结构,作者的方法可以是基于顶点邻域的,也可以是基于三角形的.这两个过程可以迭代进行,直至得到满足要求的结果.与以往的算法相比,文中算法能保证结果收敛,迭代次数更少,且能得到更好的结果.
Developable surface has zero Gaussian curvature at every point and has lots of good properties. It has been widely used in various applications in industry. Therefore, it is practically useful and important to approximate mesh surfaces using developable surfaces or near-developable surfaces. This paper presents an efficient algorithm for generating a near developable mesh surface to approximate a given mesh surface as close as possible while preserving the local structures of the surface. First, the initial mesh is obtained by using the least-norm method. The initial mesh has good developability property but it does not preserve the local structure well. Then the as-rigid-as-possible （ARAP） approach is used to optimize the initial mesh by preserving the local structures of the original mesh. This paper proposes two methods, i.e. the celt-based and the triangle-based, to preserve the local structures in the ARAP approach. Both methods work well in above algorithm. The initial mesh and the ARAP optimization can be applied in an iterative way. Experimental results show that the algorithm is convergent has obtained better results with less iterations than the previous methods.
出处
《计算机学报》
EI
CSCD
北大核心
2010年第5期927-934,共8页
Chinese Journal of Computers
基金
国家自然科学基金委员会与微软亚洲研究院联合基金(60776799)
国家"九七三"重点基础研究发展规划项目基金(2009CB320801)资助~~
关键词
可展曲面
尽可能刚性
最小范数法
最小二乘法
迭代
developable surface as-rigid-as-possible
least-norm least-squares method
iteration
