Discrete Invariants of Curves and Surfaces

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The book explores the construction of signatures for curves and surfaces, focusing on both smooth and discrete cases. It emphasizes the identification of differential and discrete invariants as coordinates for these signatures. The study delves into variational problems related to smooth and B-spline approximated curves, particularly in the context of curve completion in 2D and 3D. Solutions to the Euler-Lagrange equations are examined, along with aesthetically pleasing discrete solutions. Additionally, it discusses the integration of moving frames with Conformal Geometric Algebra for solving curve completion issues.