Rapid blending of closed curves based on curvature flow

We propose a novel closed curve blending technique that describes continuous and gradual transitions between a pair of closed curves in a plane. The main contribution of this study is to formulate the closed curve blending problem in terms of curvature flow. In this formulation, closed curve blending can be represented as a simple linear flow under linear constraints. This approach enables rapid blending, which is preferred in the production of 2D animation. In the case of curves with different turning numbers, our technique also offers smooth blending by suppressing sharp changes in the tangent vector by incorporating the curvature smoothing flow. This has not been realized with previous methods. We conducted experiments and confirmed that our technique achieved aesthetic blending in under a tenth of a second, two orders of magnitude reduction in computation time compared to state-of-the-art methods.