On Planar Shape Interpolation With Logarithmic Metric Blending

摘要

We present an interpolation method for planar shapes using logarithmic metric blending. Our approach generalizes prior work on pullback metrics to a framework, allowing us to employ different techniques, such as logarithmic blending of symmetric positive definite matrices, to have precise control over both conformal and area distortions. Key contributions include generalizing the continuous blending scheme and its adaptation to discrete mesh interpolation through different conformal and isometric parameterizations. Experimental results demonstrate that our method outperforms existing techniques in achieving bounded distortions, making it a compelling choice for applications in animation and morphing.