Mesh editing with poisson-based gradient field manipulation

ACM Trans. Graph., no. 3 (2004): 644-651

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摘要

In this paper, we introduce a novel approach to mesh editing with the Poisson equation as the theoretical foundation. The most distinctive feature of this approach is that it modifies the original mesh geometry implicitly through gradient field manipulation. Our approach can produce desirable and pleasing results for both global and local...更多

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简介
  • Mesh editing has long been an active research area in computer graphics. Most existing techniques, such as deformation, Boolean operations, detail editing and transfer, manipulate vertex positions explicitly.
  • The authors introduce a new mesh editing technique based on gradient field manipulation which implicitly modifies vertex positions
  • This technique is capable of producing desirable results with a small amount of user interaction.
  • The Poisson equation can be viewed as an alternative formulation of a least-squares minimization
  • With these appealing characteristics, editing a function can be achieved by modifying its gradient field and boundary condition, and a succeeding reconstruction using the Poisson equation.
  • Emerging from Isaac Newton’s law of gravitation [Tohline 1999], the Poisson equation with Dirichlet boundary condition is formulated as
重点内容
  • Mesh editing has long been an active research area in computer graphics
  • We introduce a new mesh editing technique based on gradient field manipulation which implicitly modifies vertex positions
  • The theoretical foundation of our technique is the Poisson equation which is able to reconstruct a scalar function from a guidance vector field and a boundary condition
  • We have developed a basic framework along with interactive tools for mesh editing
  • The product is a versatile mesh editing system that can be used for high-end applications which require superior results
结论
  • The authors have developed a basic framework along with interactive tools for mesh editing.
  • The core of the technique is a Poisson mesh solver which has a solid theoretical foundation.
  • The interactive tools are intuitive, and do not require special knowledge about the underlying theory.
  • The product is a versatile mesh editing system that can be used for high-end applications which require superior results.
  • The authors would like to overcome the limitations of the framework presented in this paper.
  • It is possible to improve the performance of the user-guided deformation by exploiting multi-grid methods
基金
  • Yizhou Yu was supported by NSF (CCR-0132970)
  • Hujun Bao was supported by NSFC (No 60021201 and 60033010) and 973 Program of China (No 2002CB312104)
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