Poisson-based curve blending

Abstract

In this paper, we introduce a novel blending approach for both 2D and 3D curves with the discrete Poisson equation defined on piecewise linear curves as the theoretical foundation. Based on defining local frames on source and target curves, a non-linear gradient field interpolation algorithm is proposed. With user-specified boundary conditions, the in-between curves are reconstructed implicitly from the interpolated gradient fields. By viewing the source curve and the target one as scalar fields defined on the common domain, our algorithm has the distinctive feature that it generates blending sequences via manipulating gradient fields instead of interpolating node coordinates. Statistics of the perimeter and the interior area (for 2D curves) show our method keeps the in-between curves as rigid as possible. Compared with competing methods, our method is more stable.