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Our method starts with a spline-based rigging system in which artists can draw and articulate sparse curvenets that describe surface profiles. By analyzing the layout of the rigged curvenets, we quantify the deformation along each curve side independent of the mesh connectivity, thus separating the articulation controllers from the underlying surface representation. To propagate the curvenet articulation over the character surface, we formulate a deformation optimization that reconstructs surface details while conforming to the rigged curvenets. In this process, we introduce a cut-cell algorithm that binds the curvenet to the surface mesh by cutting mesh elements into smaller polygons possibly with cracks, and then derive a cut-aware numerical discretization that provides harmonic interpolations with curve discontinuities. 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