Three-dimensional deformation in curl vector field

Deformation is an important research topic in graphics. There are two key issues in mesh deformation: (1) self-intersection and (2) volume preserving. In this paper, we present a new method to construct a vector field for volume-preserving mesh deformation of free-form objects. Volume-preserving is an inherent feature of a curl vector field. Since the field lines of the curl vector field will never intersect with each other, a mesh deformed under a curl vector field can avoid self-intersection between field lines. Designing the vector field based on curl is useful in preserving graphic features and preventing self-intersection. Our proposed algorithm introduces distance field into vector field construction; as a result, the shape of the curl vector field is closely related to the object shape. We define the construction of the curl vector field for translation and rotation and provide some special effects such as twisting and bending. Taking into account the information of the object, this approach can provide easy and intuitive construction for free-form objects. Experimental results show that the approach works effectively in real-time animation.