Welcome to Journal of Graphics share: 

Journal of Graphics ›› 2023, Vol. 44 ›› Issue (1): 158-165.DOI: 10.11996/JG.j.2095-302X.2023010158

• Computer Graphics and Virtual Reality • Previous Articles     Next Articles

Edge length based 3D shape interpolation

LIU Zhen-ye(), CHEN Ren-jie(), LIU Li-gang   

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei Anhui 230022, China
  • Received:2022-06-16 Revised:2022-08-06 Online:2023-10-31 Published:2023-02-16
  • Contact: CHEN Ren-jie
  • About author:LIU Zhen-ye (1997-), master student. His main research interest covers digital geometry processing. E-mail:lzy1997@mail.ustc.edu.cn
  • Supported by:
    National Natural Science Foundation of China(62072422);National Natural Science Foundation of China(62025207);Natural Science Foundation of Anhui Province(2008085MF195)

Abstract:

Shape interpolation is of important and fundamental significance to computer graphics and geometry processing, which is widely employed in computer animation and other fields. It is noted that for planar triangular meshes and 3D tetrahedral meshes, interpolating squared edge lengths is equivalent to interpolating pullback metric. Therefore, it has the good property that isometric distortion and conformation distortion are bounded simultaneously. A triangular mesh interpolation algorithm based on edge lengths was proposed by extending that to triangular meshes. Given the edge lengths, the edge length error energy was optimized using Newton's method in the stage of mesh reconstruction. In addition, the costly eigenvalue decomposition could be avoided by giving the analytic positive definite form of its Hessian matrix. It was noted that the interpolation of squared edge lengths of the tetrahedral meshes resulted in very low curvature, meaning that it could be flattened and embedded in 3D space with only a few modifications. Therefore, we proposed to first convert the triangular meshes into tetrahedral meshes, and then extract the surface from the interpolation result of the tetrahedral meshes. After that the surface served as an initialization on the Newton iteration of the edge length error energy, thus bringing the convergence result closer to the global optimum. Experiments performed on a series of triangular meshes show that the proposed method leads to smaller edge length error than that of previous edge length-based methods, and that the results obtained have bounded distortion.

Key words: morphing, shape interpolation, computer graphics, triangular mesh

CLC Number: