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Digital Geometry by Azriel Rosenfeld, Reinhard Klette

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CHAPTER 12

3D Arc Length, Surface Area, and Curvature

Length and curvature estimation for arcs in 2D spaces were treated in Chapter 10. This chapter begins by discussing length, curvature, and torsion estimation for arcs in 3D spaces. It then discusses how the area or curvature of a surface can be estimated using either polyhedrization of the surface or estimation of the surface normal. Estimation methods can be classified as local or global; such a classification can also be used in other contexts. Estimators can be evaluated in terms of their multigrid convergence and their computational complexity. Local methods are fast, but their accuracy is limited. Global methods are more complex, but they can potentially provide accurate estimates.

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