准共形映射的三维模型变形算法

3D model deformation algorithm for quasi-conformal mapping

为了解决在三维曲面之间直接变形艰难、局部区域失真较大、对细节丰富或骨架不明显的模型变形效果差的问题,提出一种基于准共形映射的三维模型变形算法。首先,采用准共形映射将三维模型参数化到二维平面圆盘;其次,基于准共形迭代算法计算2个二维平面圆盘之间的映射,构建变形后的二维模型;最后,采用模型恢复算法从变形后的二维模型还原出三维模型,从而得到具有不同外观的三维模型。实验选取了2个公开数据集中的三维模型进行变形操作,并与基于拉普拉斯的微分坐标变形算法进行了对比。结果表明,该方法可以便捷地对模型进行平移、旋转和拉伸等操作,很好地保持了模型的局部特征,运行时间短,变形效果好,鲁棒性强。此方法能够适用于具有任意边界的模型,对模型的选取要求低,适用于各类三维模型的变形及三维模型的快速构造。

In order to solve the problems of difficult direct deformation between three-dimensional surfaces,large distortion of local areas,and poor deformation effect of models with rich details or not obvious skeleton,a 3D model deformation algorithm based on quasi-conformal mapping was proposed.Firstly,the 3D model was parameterized to a 2D plane disk using quasi-conformal mapping.Secondly,the quasi-common iterative algorithm was used to calculate the mapping between two 2D plane disks to construct the deformed 2D model.Finally,the 2D→3D model restoration algorithm was proposed to restore the 3D model from the deformed 2D model,thereby obtaining a 3D model with different appearances.In the experiment,3D models from two public datasets were selected for deformation operation,and the proposed method was compared with Laplacian-based differential coordinate deformation algorithm.The results show that the proposed method can perform a series of operations such as translation,rotation and stretching.The local features of the model are well maintained with short running time,good deformation effect and strong robustness.The method proposed can be applied to the model with any boundary and has low requirements for model selection.It is suitable for the deformation of various 3D models and the rapid construction of 3D models.