中文摘要：

为了对二维平面形状进行变形,提出一种高效的基于自适应细分策略的保刚性变形方法.首先通过显式求解变形问题中需要的旋转矩阵,使其计算效率高于原始的采用SVD分解来计算旋转矩阵的方法;其次采用一种局部的细分策略,对在变形过程中遭受拉伸扭曲较为剧烈的区域中的三角片进行自适应的加细可以显著地减少输入网格的扭曲程度,获得更好的变形结果.文中方法对传统的ARAP变形方法上进行了改善,使之在变形结果的质量和算法的效率之间达到较为理想的平衡状态.

英文摘要：

This paper presents an efficient as-rigid-as-possible（ARAP） deformation method for planar shape deformation.First,an explicit formula for computing the rotation matrices used in the deformation is introduced,which is more efficient than the previous method based on singular value decomposition（SVD） computation.Second,a local subdivision scheme is proposed to adaptively refine the triangles in regions with large distortions.It can largely reduce distortion in these regions and generate high quality deformation results.Experimental results have shown that the improved deformation method has obtained a good trade-off between deformation quality and computation efficiency.