Poisson shape interpolation

ABSTRACT

In this paper, we propose a novel shape interpolation approach based on Poisson equation. We formulate the trajectory problem of shape interpolation as solving Poisson equations defined on a domain mesh. A non-linear gradient field interpolation method is proposed to take both vertex coordinates and surface orientation into account. With proper boundary conditions, the in-between shapes are reconstructed implicitly from the interpolated gradient fields, while traditional methods usually manipulate vertex coordinates directly. Besides of global shape interpolation, our method is also applicable to local shape interpolation, and can be further enhanced by incorporating with deformation. Our approach can generate visual pleasing and physical plausible morphing sequences with stable area and volume changes. Experimental results demonstrate that our technique can avoid the shrinkage problem appeared in linear shape interpolation.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Curve, surface, solid, and object representations

Keywords:
domain mesh, gradient field manipulation, poisson equation, shape interpolation, trajectory problem