We present a computational tool for designing ornamental curve networks—structurally-sound physical surfaces with user-controlled aesthetics. In contrast to approaches that leverage texture synthesis for creating decorative surface patterns, our method relies on user-defined spline curves as central design primitives. More specifically, we build on the physically-inspired metaphor of an embedded elastic curve that can move on a smooth surface, deform, and connect with other curves. We formalize this idea as a globally coupled energy-minimization problem, discretized with piece-wise linear curves that are optimized in the parametric space of a smooth surface. Building on this technical core, we propose a set of interactive design and editing tools that we demonstrate on manually-created layouts and semi-automated deformable packings. In order to prevent excessive compliance, we furthermore propose a structural analysis tool that uses eigenanalysis to identify potentially large deformations between geodesically-close curves and guide the user in strengthening the corresponding regions. We used our approach to create a variety of designs in simulation, validated with a set of 3D-printed physical prototypes.
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