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This paper presents an accurate, very fast approach for the deformations of two-dimensional physically based shape models representing open and closed curves. The introduced models are much faster than other deformable models (e.g., finite-element methods). The approach relies on the determination of explicit deformation governing equations that involve neither eigenvalue decomposition, nor any other computationally intensive numerical operation. The approach was evaluated and compared with another fast and accurate physics-based deformable shape model, both in terms of deformation accuracy and computation time. The conclusion is that the introduced model is completely accurate and is deformed very fast on current personal computers (Pentium III), achieving more than 380 contour deformations per second.