Real-time surface manipulation with C1 continuity through simple and efficient physics-based deformations

Shuangbu Wang, Nan Xiang, Yu Xia*, Lihua You, Jianjun Zhang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We present a novel but simple physics-based method to interactively manipulate surface shapes of 3D models with C1 continuity in real time. A fourth-order partial differential equation involving a sculpting force originating from elastic bending of thin plates is proposed to define physics-based deformations and achieve C1 continuity at the boundary of deformation regions. In order to obtain real-time physics-based surface manipulation, we construct a mapping relationship between a deformation region in a 3D coordinate space and a unit circle on a 2D parametric plane, formulate corresponding C1 continuous boundary conditions for the unit circle, and obtain a simple analytical solution to describe the physics-based deformation in the unit circle caused by a sculpting force. After that, the obtained physics-based deformation is mapped back to the 3D coordinate space, and added to the original surface to create a new surface shape with C1 continuity at the boundary of the deformation region. We also develop an interactive user interface as a plug-in of the 3D modelling software package Maya to achieve real-time surface manipulation. The effectiveness, easiness, real-time performance, and better realism of our proposed method is demonstrated by testing surface deformations on several 3D models and comparing with other methods and ground-truth deformations.

Original languageEnglish
Pages (from-to)2741-2753
Number of pages13
JournalVisual Computer
Issue number9-11
Publication statusPublished - Sept 2021
Externally publishedYes


  • Mapping
  • Partial differential equation
  • Physics-based deformations
  • Surface manipulation
  • User interface

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