Localized quasi-(bi)harmonic field and its applications

(Bi)harmonic field has wide applications in geometry processing. Traditionally, to locally control the influence region of a (bi)harmonic field, users usually need to determine the range of its support, regions with non-zero scalar values, by prescribing appropriate boundary conditions. However, this way is non-intuitive and inconvenient. We proposed localized quasi-(bi)harmonic field, which is achieved through a ℓ1-norm regularized convex optimization. It can conveniently control the local support of the scalar field while still keeping some nice properties of the (bi)harmonic field. We applied the localized quasi-(bi)harmonic field in applications such as shape deformation and shape merging, and the experiment results show its benefits.