Abstract: In order to maintain the details of the 3D model, correct the problem of distortion and folding of the as-rigid-as-possible (ARAP) mesh deformation used in large and nonperfect rigid deformation, an ARAP deformation method is proposed based on geometric field in heat. First, the Laplacian deformation of the model is carried out. On this basis, the rotation matrix of local cell is solved by singular value decomposition, and the rigid deformation energy of the model is calculated. Then by solving the sparse linear system, the deformation points are updated. By solving the two-time sparse linear system, we calculate the geometric field deviation of the deformation process, and correct the deformed mesh to get the deformation results close to those of the original mesh. Iterate the above steps until the geometric field deviation to meet certain requirements, and finally the final deformation results are obtained. The example shows that the method can quickly complete the mesh point correction function in mesh deformation process, and it can also effectively avoid grid collapse when applied to large-scale deformation.

Key words: as-rigid-as-possible mesh deformation, geometric field in heat, sparse linear system, folding