Shape interpolation is essential in graphics and geometry processing. For instance, smoothly transitioning between two poses of the same shape is crucial for animation, while morphing multiple shapes helps with design exploration. Since the blended shapes often differ, some distortion is unavoidable.
We introduce an interpolation method for planar shapes based on logarithmic metric blending. Our approach extends previous work on pullback metrics, enabling the use of various techniques - such as our proposed logarithmic blending - to precisely control both conformal and area distortions. A key contribution is the adaptation to discrete mesh interpolation through different conformal, isometric and equiareal parameterizations. Experimental results show that our method surpasses existing techniques in maintaining bounded distortions, making it an effective option for applications in animation and morphing.
