Free-form deformations via sketching and manipulating scalar fields

This paper presents a novel Scalar-field based Free-Form Deformation (SFFD) technique founded upon general flow constraints and implicit functions. In contrast to the traditional lattice-based FFD driven by parametric geometry and spline theory, we employ scalar fields as embedding spaces instead. Upon the deformation of the scalar field, the vertices will move accordingly, which result in free-form deformations of the embedded object. The scalar field construction, sketching, and manipulation are both natural and intuitive. By tightly coupling self-adaptive subdivision and mesh optimization with SFFD, versatile multi-resolution free-form deformations can be achieved because our algorithm can adaptively refine and improve the model on the fly to improve the mesh quality. We can also enforce various constraints on embedded models, which enable our technique to preserve the shape features and facilitate more sophisticated design. Our system demonstrates that SFFD is very powerful and intuitive for shape modeling. It significantly enhances traditional FFD techniques and facilitates a larger number of shape deformations.