Curvature continuity of curves at nodepoints is required in modeling tangent-plane and curvature continuous n-sided surfaces and surfaces over arbitrary curve meshes. This paper provides methods for optimal modification of curves at a common nodepoint, to make them tangent-plane and curvature continuous at the nodepoint. These methods can also be used to optimally estimate the intrinsic measures such as the Gaussian and mean curvatures of surfaces with discrete line and curve mesh representations such as triangular meshes.

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