Linear rotation-invariant coordinates for meshes

Yaron Lipman*, Olga Sorkine, David Levin, Daniel Cohen-Or

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review


We introduce a rigid motion invariant mesh representation based on discrete forms defined on the mesh. The reconstruction of mesh geometry from this representation requires solving two sparse linear systems that arise from the discrete forms: the first system defines the relationship between local frames on the mesh, and the second encodes the position of the vertices via the local frames. The reconstructed geometry is unique up to a rigid transformation of the mesh. We define surface editing operations by placing user-defined constraints on the local frames and the vertex positions. These constraints are incorporated in the two linear reconstruction systems, and their solution produces a deformed surface geometry that preserves the local differential properties in the least-squares sense. Linear combination of shapes expressed with our representation enables linear shape interpolation that correctly handles rotations. We demonstrate the effectiveness of the new representation with various detail-preserving editing operators and shape morphing.

Original languageEnglish
Pages (from-to)479-487
Number of pages9
JournalACM Transactions on Graphics
Issue number3
StatePublished - Jul 2005
EventACM SIGGRAPH 2005 - Los Angeles, CA, United States
Duration: 31 Jul 20054 Aug 2005


  • Local frames
  • Mesh editing
  • Rigid-motion invariant shape representation
  • Shape blending


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